On Dynamical Poisson Groupoids I

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821865460
Total Pages : 92 pages
Book Rating : 4.8/5 (654 download)

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Book Synopsis On Dynamical Poisson Groupoids I by : Serge Parmentier

Download or read book On Dynamical Poisson Groupoids I written by Serge Parmentier and published by American Mathematical Soc.. This book was released on 2005-01-27 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: We address the question of duality for the dynamical Poisson groupoids of Etingof and Varchenko over a contractible base. We also give an explicit description for the coboundary case associated with the solutions of (CDYBE) on simple Lie algebras as classified by the same authors. Our approach is based on the study of a class of Poisson structures on trivial Lie groupoids within the category of biequivariant Poisson manifolds. In the former case, it is shown that the dual Poisson groupoid of such a dynamical Poisson groupoid is isomorphic to a Poisson groupoid (with trivial Lie groupoid structure) within this category. In the latter case, we find that the dual Poisson groupoid is also of dynamical type modulo Poisson groupoid isomorphisms. For the coboundary dynamical Poisson groupoids associated with constant $r$-matrices, we give an explicit construction of the corresponding symplectic double groupoids. In this case, the symplectic leaves of the dynamical Poisson groupoid are shown to be the orbits of a Poisson Lie group action.

On Dynamical Poisson Groupoids

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ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (16 download)

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Book Synopsis On Dynamical Poisson Groupoids by : Luen-Chau Li

Download or read book On Dynamical Poisson Groupoids written by Luen-Chau Li and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

On Dynamical Poisson Groupoids I

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821836730
Total Pages : 86 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis On Dynamical Poisson Groupoids I by : Luen-Chau Li

Download or read book On Dynamical Poisson Groupoids I written by Luen-Chau Li and published by American Mathematical Soc.. This book was released on 2005 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: We address the question of duality for the dynamical Poisson groupoids of Etingof and Varchenko over a contractible base. We also give an explicit description for the coboundary case associated with the solutions of (CDYBE) on simple Lie algebras as classified by the same authors.

On Dynamical Poisson Groupoids I

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Publisher :
ISBN 13 : 9781470404253
Total Pages : 72 pages
Book Rating : 4.4/5 (42 download)

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Book Synopsis On Dynamical Poisson Groupoids I by : Luen-Chau Li

Download or read book On Dynamical Poisson Groupoids I written by Luen-Chau Li and published by . This book was released on 2014-09-11 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: We address the question of duality for the dynamical Poisson groupoids of Etingof and Varchenko over a contractible base. We also give an explicit description for the coboundary case associated with the solutions of (CDYBE) on simple Lie algebras as classified by the same authors.

Groupoids in Analysis, Geometry, and Physics

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Publisher : American Mathematical Soc.
ISBN 13 : 0821820427
Total Pages : 208 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Groupoids in Analysis, Geometry, and Physics by : Arlan Ramsay

Download or read book Groupoids in Analysis, Geometry, and Physics written by Arlan Ramsay and published by American Mathematical Soc.. This book was released on 2001 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Groupoids often occur when there is symmetry of a nature not expressible in terms of groups. Other uses of groupoids can involve something of a dynamical nature. Indeed, some of the main examples come from group actions. It should also be noted that in many situations where groupoids have been used, the main emphasis has not been on symmetry or dynamics issues. While the implicit symmetry and dynamics are relevant, the groupoid records mostly the structure of the space of leaves and the holonomy. More generally, the use of groupoids is very much related to various notions of orbit equivalance. This book presents the proceedings from the Joint Summer Research Conference on ``Groupoids in Analysis, Geometry, and Physics'' held in Boulder, CO. The book begins with an introduction to ways in which groupoids allow a more comprehensive view of symmetry than is seen via groups. Topics range from foliations, pseudo-differential operators, $KK$-theory, amenability, Fell bundles, and index theory to quantization of Poisson manifolds. Readers will find examples of important tools for working with groupoids. This book is geared to students and researchers. It is intended to improve their understanding of groupoids and to encourage them to look further while learning about the tools used.

Poisson Structures

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Publisher : Springer Science & Business Media
ISBN 13 : 3642310907
Total Pages : 470 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Poisson Structures by : Camille Laurent-Gengoux

Download or read book Poisson Structures written by Camille Laurent-Gengoux and published by Springer Science & Business Media. This book was released on 2012-08-27 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Poisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of these contexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to the problem in nearly all cases. Poisson Structures is the first book that offers a comprehensive introduction to the theory, as well as an overview of the different aspects of Poisson structures. The first part covers solid foundations, the central part consists of a detailed exposition of the different known types of Poisson structures and of the (usually mathematical) contexts in which they appear, and the final part is devoted to the two main applications of Poisson structures (integrable systems and deformation quantization). The clear structure of the book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researchers who are interested in an introduction to the many facets and applications of Poisson structures.​

Hopf Algebras and Generalizations

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Publisher : American Mathematical Soc.
ISBN 13 : 0821838202
Total Pages : 186 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Hopf Algebras and Generalizations by : Louis H. Kauffman

Download or read book Hopf Algebras and Generalizations written by Louis H. Kauffman and published by American Mathematical Soc.. This book was released on 2007 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hopf algebras have proved to be very interesting structures with deep connections to various areas of mathematics, particularly through quantum groups. Indeed, the study of Hopf algebras, their representations, their generalizations, and the categories related to all these objects has an interdisciplinary nature. It finds methods, relationships, motivations and applications throughout algebra, category theory, topology, geometry, quantum field theory, quantum gravity, and also combinatorics, logic, and theoretical computer science. This volume portrays the vitality of contemporary research in Hopf algebras. Altogether, the articles in the volume explore essential aspects of Hopf algebras and some of their best-known generalizations by means of a variety of approaches and perspectives. They make use of quite different techniques that are already consolidated in the area of quantum algebra. This volume demonstrates the diversity and richness of its subject. Most of its papers introduce the reader to their respective contexts and structures through very expository preliminary sections.

General Theory of Lie Groupoids and Lie Algebroids

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Publisher : Cambridge University Press
ISBN 13 : 0521499283
Total Pages : 540 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis General Theory of Lie Groupoids and Lie Algebroids by : Kirill C. H. Mackenzie

Download or read book General Theory of Lie Groupoids and Lie Algebroids written by Kirill C. H. Mackenzie and published by Cambridge University Press. This book was released on 2005-06-09 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: This a comprehensive modern account of the theory of Lie groupoids and Lie algebroids, and their importance in differential geometry, in particular their relations with Poisson geometry andgeneral connection theory. It covers much work done since the mid 1980s including the first treatment in book form of Poisson groupoids, Lie bialgebroids and double vector bundles. As such, this book will be of great interest to all those working in or wishing to learn the modern theory of Lie groupoids and Lie algebroids.

An Analogue of a Reductive Algebraic Monoid Whose Unit Group Is a Kac-Moody Group

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Publisher : American Mathematical Soc.
ISBN 13 : 082183648X
Total Pages : 104 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis An Analogue of a Reductive Algebraic Monoid Whose Unit Group Is a Kac-Moody Group by : Claus Mokler

Download or read book An Analogue of a Reductive Algebraic Monoid Whose Unit Group Is a Kac-Moody Group written by Claus Mokler and published by American Mathematical Soc.. This book was released on 2005 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: By an easy generalization of the Tannaka-Krein reconstruction we associate to the category of admissible representations of the category ${\mathcal O}$ of a Kac-Moody algebra, and its category of admissible duals, a monoid with a coordinate ring. The Kac-Moody group is the Zariski open dense unit group of this monoid. The restriction of the coordinate ring to the Kac-Moody group is the algebra of strongly regular functions introduced by V. Kac and D. Peterson. This monoid has similar structural properties as a reductive algebraic monoid. In particular it is unit regular, its idempotents related to the faces of the Tits cone. It has Bruhat and Birkhoff decompositions. The Kac-Moody algebra is isomorphic to the Lie algebra of this monoid.

A Categorical Approach to Imprimitivity Theorems for $C^*$-Dynamical Systems

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Publisher : American Mathematical Soc.
ISBN 13 : 0821838571
Total Pages : 186 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis A Categorical Approach to Imprimitivity Theorems for $C^*$-Dynamical Systems by : Siegfried Echterhoff

Download or read book A Categorical Approach to Imprimitivity Theorems for $C^*$-Dynamical Systems written by Siegfried Echterhoff and published by American Mathematical Soc.. This book was released on 2006 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has become apparent that studying the representation theory and structure of crossed-product C*-algebras requires imprimitivity theorems. This monograph shows that the imprimitivity theorem for reduced algebras, Green's imprimitivity theorem for actions of groups, and Mansfield's imprimitivity theorem for coactions of groups can all be understoo

Quantum Groups

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Publisher : American Mathematical Soc.
ISBN 13 : 0821837133
Total Pages : 352 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Quantum Groups by : Pavel I. Etingof

Download or read book Quantum Groups written by Pavel I. Etingof and published by American Mathematical Soc.. This book was released on 2007 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume are based on the talks given at the conference on quantum groups dedicated to the memory of Joseph Donin, which was held at the Technion Institute, Haifa, Israel in July 2004. A survey of Donin's distinguished mathematical career is included. Several articles, which were directly influenced by the research of Donin and his colleagues, deal with invariant quantization, dynamical $R$-matrices, Poisson homogeneous spaces, and reflection equation algebras. The topics of other articles include Hecke symmetries, orbifolds, set-theoretic solutions to the pentagon equations, representations of quantum current algebras, unipotent crystals, the Springer resolution, the Fourier transform on Hopf algebras, and, as a change of pace, the combinatorics of smoothly knotted surfaces. The articles all contain important new contributions to their respective areas and will be of great interest to graduate students and research mathematicians interested in Hopf algebras, quantum groups, and applications. Information for our distributors: This book is copublished with Bar-Ilan University (Ramat-Gan, Israel).

Integrable Hamiltonian Systems on Complex Lie Groups

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Publisher : American Mathematical Soc.
ISBN 13 : 0821837648
Total Pages : 150 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Integrable Hamiltonian Systems on Complex Lie Groups by : Velimir Jurdjevic

Download or read book Integrable Hamiltonian Systems on Complex Lie Groups written by Velimir Jurdjevic and published by American Mathematical Soc.. This book was released on 2005 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies the elastic problems on simply connected manifolds $M_n$ whose orthonormal frame bundle is a Lie group $G$. This title synthesizes ideas from optimal control theory, adapted to variational problems on the principal bundles of Riemannian spaces, and the symplectic geometry of the Lie algebra $\mathfrak{g}, $ of $G$

Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations

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Publisher : American Mathematical Soc.
ISBN 13 : 0821837710
Total Pages : 126 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations by : Greg Hjorth

Download or read book Rigidity Theorems for Actions of Product Groups and Countable Borel Equivalence Relations written by Greg Hjorth and published by American Mathematical Soc.. This book was released on 2005 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contributes to the theory of Borel equivalence relations, considered up to Borel reducibility, and measures preserving group actions considered up to orbit equivalence. This title catalogs the actions of products of the free group and obtains additional rigidity theorems and relative ergodicity results in this context.

A Generating Function Approach to the Enumeration of Matrices in Classical Groups over Finite Fields

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Publisher : American Mathematical Soc.
ISBN 13 : 0821837060
Total Pages : 104 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis A Generating Function Approach to the Enumeration of Matrices in Classical Groups over Finite Fields by : Jason Fulman

Download or read book A Generating Function Approach to the Enumeration of Matrices in Classical Groups over Finite Fields written by Jason Fulman and published by American Mathematical Soc.. This book was released on 2005 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generating function techniques are used to study the probability that an element of a classical group defined over a finite field is separable, cyclic, semisimple or regular. The limits of these probabilities as the dimension tends to infinity are calculated in all cases, and exponential convergence to the limit is proved. These results complement and extend earlier results of the authors, G. E. Wall, and Guralnick & Lubeck.

Quasi-Ordinary Power Series and Their Zeta Functions

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Publisher : American Mathematical Soc.
ISBN 13 : 0821838768
Total Pages : 98 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Quasi-Ordinary Power Series and Their Zeta Functions by : Enrique Artal-Bartolo

Download or read book Quasi-Ordinary Power Series and Their Zeta Functions written by Enrique Artal-Bartolo and published by American Mathematical Soc.. This book was released on 2005 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intends to prove the monodromy conjecture for the local Igusa zeta function of a quasi-ordinary polynomial of arbitrary dimension defined over a number field. In order to do it, this title computes the local Denef-Loeser motivic zeta function $Z_{\text{DL}}(h, T)$ of a quasi-ordinary power series $h$ of arbitrary dimension

A Random Tiling Model for Two Dimensional Electrostatics

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Publisher : American Mathematical Soc.
ISBN 13 : 082183794X
Total Pages : 162 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis A Random Tiling Model for Two Dimensional Electrostatics by : Mihai Ciucu

Download or read book A Random Tiling Model for Two Dimensional Electrostatics written by Mihai Ciucu and published by American Mathematical Soc.. This book was released on 2005 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies the correlation of holes in random lozenge (i.e., unit rhombus) tilings of the triangular lattice. This book analyzes the joint correlation of these triangular holes when their complement is tiled uniformly at random by lozenges.

Weil-Petersson Metric on the Universal Teichmuller Space

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Publisher : American Mathematical Soc.
ISBN 13 : 0821839365
Total Pages : 136 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Weil-Petersson Metric on the Universal Teichmuller Space by : Leon Armenovich Takhtadzhi︠a︡n

Download or read book Weil-Petersson Metric on the Universal Teichmuller Space written by Leon Armenovich Takhtadzhi︠a︡n and published by American Mathematical Soc.. This book was released on 2006 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this memoir, we prove that the universal Teichmuller space $T(1)$ carries a new structure of a complex Hilbert manifold and show that the connected component of the identity of $T(1)$ -- the Hilbert submanifold $T {0 (1)$ -- is a topological group. We define a Weil-Petersson metric on $T(1)$ by Hilbert space inner products on tangent spaces, compute its Riemann curvature tensor, and show that $T(1)$ is a Kahler-Einstein manifold with negative Ricci and sectional curvatures. We introduce and compute Mumford-Miller-Morita characteristic forms for the vertical tangent bundle of the universal Teichmuller curve fibration over the universal Teichmuller space. As an application, we derive Wolpert curvature formulas for the finite-dimensional Teichmuller spaces from the formulas for the universal Teichmuller space. We study in detail the Hilbert manifold structure on $T {0 (1)$ and characterize points on $T {0 (1)$ in terms of Bers and pre-Bers embeddings by proving that the Grunsky operators $B {1 $ and The results of this memoir were presented in our e-prints: Weil-Petersson metric on the universal Teichmuller space I. Curvature properties and Chern forms, arXiv:math.CV/0312172 (2003), and Weil-Petersson metric on the universal Teichmuller space II. Kahler potential and period mapping, arXiv:math.CV/0406408 (2004).