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An Analogue Of A Reductive Algebraic Monoid Whose Unit Group Is A Kac Moody Group
Download An Analogue Of A Reductive Algebraic Monoid Whose Unit Group Is A Kac Moody Group full books in PDF, epub, and Kindle. Read online An Analogue Of A Reductive Algebraic Monoid Whose Unit Group Is A Kac Moody Group ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
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.
Book Synopsis Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics by : Mahir Can
Download or read book Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics written by Mahir Can and published by Springer. This book was released on 2014-06-11 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of fifteen articles and is dedicated to the sixtieth birthdays of Lex Renner and Mohan Putcha, the pioneers of the field of algebraic monoids. Topics presented include: structure and representation theory of reductive algebraic monoids monoid schemes and applications of monoids monoids related to Lie theory equivariant embeddings of algebraic groups constructions and properties of monoids from algebraic combinatorics endomorphism monoids induced from vector bundles Hodge–Newton decompositions of reductive monoids A portion of these articles are designed to serve as a self-contained introduction to these topics, while the remaining contributions are research articles containing previously unpublished results, which are sure to become very influential for future work. Among these, for example, the important recent work of Michel Brion and Lex Renner showing that the algebraic semi groups are strongly π-regular. Graduate students as well as researchers working in the fields of algebraic (semi)group theory, algebraic combinatorics and the theory of algebraic group embeddings will benefit from this unique and broad compilation of some fundamental results in (semi)group theory, algebraic group embeddings and algebraic combinatorics merged under the umbrella of algebraic monoids.
Book Synopsis Linear Algebraic Monoids by : Lex E. Renner
Download or read book Linear Algebraic Monoids written by Lex E. Renner and published by Springer Science & Business Media. This book was released on 2005-03-11 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of linear algebraic monoids culminates in a coherent blend of algebraic groups, convex geometry, and semigroup theory. The book discusses all the key topics in detail, including classification, orbit structure, representations, universal constructions, and abstract analogues. An explicit cell decomposition is constructed for the wonderful compactification, as is a universal deformation for any semisimple group. A final chapter summarizes important connections with other areas of algebra and geometry. The book will serve as a solid basis for further research. Open problems are discussed as they arise and many useful exercises are included.
Book Synopsis Relatively Hyperbolic Groups: Intrinsic Geometry, Algebraic Properties, and Algorithmic Problems by : Denis V. Osin
Download or read book Relatively Hyperbolic Groups: Intrinsic Geometry, Algebraic Properties, and Algorithmic Problems written by Denis V. Osin and published by American Mathematical Soc.. This book was released on 2006 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this the authors obtain an isoperimetric characterization of relatively hyperbolicity of a groups with respect to a collection of subgroups. This allows them to apply classical combinatorial methods related to van Kampen diagrams to obtain relative analogues of some well-known algebraic and geometric properties of ordinary hyperbolic groups. There is also an introduction and study of the notion of a relatively quasi-convex subgroup of a relatively hyperbolic group and solve somenatural algorithmic problems.
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 $G$
Book Synopsis Lax-Phillips Scattering and Conservative Linear Systems: A Cuntz-Algebra Multidimensional Setting by : Joseph A. Ball
Download or read book Lax-Phillips Scattering and Conservative Linear Systems: A Cuntz-Algebra Multidimensional Setting written by Joseph A. Ball and published by American Mathematical Soc.. This book was released on 2005 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: The evolution operator for the Lax-Phillips scattering system is an isometric representation of the Cuntz algebra, while the nonnegative time axis for the conservative, linear system is the free semigroup on $d$ letters. This title presents a multivariable setting for Lax-Phillips scattering and for conservative, discrete-time, linear systems.
Book Synopsis The Hilbert Function of a Level Algebra by : A. V. Geramita
Download or read book The Hilbert Function of a Level Algebra written by A. V. Geramita and published by American Mathematical Soc.. This book was released on 2007 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let $R$ be a polynomial ring over an algebraically closed field and let $A$ be a standard graded Cohen-Macaulay quotient of $R$. The authors state that $A$ is a level algebra if the last module in the minimal free resolution of $A$ (as $R$-module) is of the form $R(-s)a$, where $s$ and $a$ are positive integers. When $a=1$ these are also known as Gorenstein algebras. The basic question addressed in this paper is: What can be the Hilbert Function of a level algebra? The authors consider the question in several particular cases, e.g., when $A$ is an Artinian algebra, or when $A$ is the homogeneous coordinate ring of a reduced set of points, or when $A$ satisfies the Weak Lefschetz Property. The authors give new methods for showing that certain functions are NOT possible as the Hilbert function of a level algebra and also give new methods to construct level algebras. In a (rather long) appendix, the authors apply their results to give complete lists of all possible Hilbert functions in the case that the codimension of $A = 3$, $s$ is small and $a$ takes on certain fixed values.
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.
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.
Book Synopsis Generative Complexity in Algebra by : Joel Berman
Download or read book Generative Complexity in Algebra written by Joel Berman and published by American Mathematical Soc.. This book was released on 2005 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Considers the behavior of $\mathrm{G}_\mathcal{C}(k)$ when $\mathcal{C}$ is a locally finite equational class (variety) of algebras and $k$ is finite. This title looks at ways that algebraic properties of $\mathcal{C}$ lead to upper or lower bounds on generative complexity.
Book Synopsis Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor $D$-Modules, Part 2 by : Takuro Mochizuki
Download or read book Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor $D$-Modules, Part 2 written by Takuro Mochizuki and published by American Mathematical Soc.. This book was released on 2007 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author studies the asymptotic behaviour of tame harmonic bundles. First he proves a local freeness of the prolongment of deformed holomorphic bundle by an increasing order. Then he obtains the polarized mixed twistor structure from the data on the divisors. As one of the applications, he obtains the norm estimate of holomorphic or flat sections by weight filtrations of the monodromies. As another application, the author establishes the correspondence of semisimple regularholonomic $D$-modules and polarizable pure imaginary pure twistor $D$-modules through tame pure imaginary harmonic bundles, which is a conjecture of C. Sabbah. Then the regular holonomic version of M. Kashiwara's conjecture follows from the results of Sabbah and the author.
Book Synopsis Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor $D$-Modules, Part 1 by : Takuro Mochizuki
Download or read book Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor $D$-Modules, Part 1 written by Takuro Mochizuki and published by American Mathematical Soc.. This book was released on 2007 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author studies the asymptotic behaviour of tame harmonic bundles. First he proves a local freeness of the prolongment of deformed holomorphic bundle by an increasing order. Then he obtains the polarized mixed twistor structure from the data on the divisors. As one of the applications, he obtains the norm estimate of holomorphic or flat sections by weight filtrations of the monodromies. As another application, the author establishes the correspondence of semisimple regular holonomic $D$-modules and polarizable pure imaginary pure twistor $D$-modules through tame pure imaginary harmonic bundles, which is a conjecture of C. Sabbah. Then the regular holonomic version of M. Kashiwara's conjecture follows from the results of Sabbah and the author.
Book Synopsis The Calculus of One-Sided $M$-Ideals and Multipliers in Operator Spaces by : David P. Blecher
Download or read book The Calculus of One-Sided $M$-Ideals and Multipliers in Operator Spaces written by David P. Blecher and published by American Mathematical Soc.. This book was released on 2006 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of one-sided $M$-ideals and multipliers of operator spaces is simultaneously a generalization of classical $M$-ideals, ideals in operator algebras, and aspects of the theory of Hilbert $C*$-modules and their maps. Here we give a systematic exposition of this theory. The main part of this memoir consists of a 'calculus' for one-sided $M$-ideals and multipliers, i.e. a collection of the properties of one-sided $M$-ideals and multipliers with respect to the basic constructions met in functional analysis. This is intended to be a reference tool for 'noncommutative functional analysts' who may encounter a one-sided $M$-ideal or multiplier in their work.
Book Synopsis Measure Theoretic Laws for lim sup Sets by : Victor Beresnevich Detta Dickinson Sanju Velani
Download or read book Measure Theoretic Laws for lim sup Sets written by Victor Beresnevich Detta Dickinson Sanju Velani and published by American Mathematical Soc.. This book was released on 2005-12-01 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given a compact metric space $(\Omega,d)$ equipped with a non-atomic, probability measure $m$ and a positive decreasing function $\psi$, we consider a natural class of lim sup subsets $\Lambda(\psi)$ of $\Omega$. The classical lim sup set $W(\psi)$ of `$\psi$-approximable' numbers in the theory of metric Diophantine approximation fall within this class. We establish sufficient conditions (which are also necessary under some natural assumptions) for the $m$-measure of $\Lambda(\psi)$ to be either positive or full in $\Omega$ and for the Hausdorff $f$-measure to be infinite. The classical theorems of Khintchine-Groshev and Jarnik concerning $W(\psi)$ fall into our general framework. The main results provide a unifying treatment of numerous problems in metric Diophantine approximation including those for real, complex and $p$-adic fields associated with both independent and dependent quantities. Applications also include those to Kleinian groups and rational maps. Compared to previous works our framework allows us to successfully remove many unnecessary conditions and strengthen fundamental results such as Jarnik's theorem and the Baker-Schmidt theorem. In particular, the strengthening of Jarnik's theorem opens up the Duffin-Schaeffer conjecture for Hausdorff measures.
Book Synopsis A Sharp Threshold for Random Graphs with a Monochromatic Triangle in Every Edge Coloring by : Ehud Friedgut
Download or read book A Sharp Threshold for Random Graphs with a Monochromatic Triangle in Every Edge Coloring written by Ehud Friedgut and published by American Mathematical Soc.. This book was released on 2006 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let $\cal{R}$ be the set of all finite graphs $G$ with the Ramsey property that every coloring of the edges of $G$ by two colors yields a monochromatic triangle. In this paper the authors establish a sharp threshold for random graphs with this property. Let $G(n, p)$ be the random graph on $n$ vertices with edge probability $p$. The authors prove that there exists a function $\widehat c=\widehat c(n)=\Theta(1)$ such that for any $\varepsilon > 0$, as $n$ tends to infinity, $Pr\left[G(n, (1-\varepsilon)\widehat c/\sqrt{n}) \in \cal{R} \right] \rightarrow 0$ and $Pr \left[ G(n, (1]\varepsilon)\widehat c/\sqrt{n}) \in \cal{R}\ \right] \rightarrow 1.$. A crucial tool that is used in the proof and is of independent interest is a generalization of Szemeredi's Regularity Lemma to a certain hypergraph setti
Book Synopsis Measure Theoretic Laws for lim sup Sets by : Victor Beresnevich
Download or read book Measure Theoretic Laws for lim sup Sets written by Victor Beresnevich and published by American Mathematical Soc.. This book was released on 2006 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given a compact metric space $(\Omega,d)$ equipped with a non-atomic, probability measure $m$ and a positive decreasing function $\psi$, we consider a natural class of lim sup subsets $\Lambda(\psi)$ of $\Omega$. The classical lim sup set $W(\psi)$ of `$\p$-approximable' numbers in the theory of metric Diophantine approximation fall within this class. We establish sufficient conditions (which are also necessary under some natural assumptions) for the $m$-measure of $\Lambda(\psi)$to be either positive or full in $\Omega$ and for the Hausdorff $f$-measure to be infinite. The classical theorems of Khintchine-Groshev and Jarník concerning $W(\psi)$ fall into our general framework. The main results provide a unifying treatment of numerous problems in metric Diophantineapproximation including those for real, complex and $p$-adic fields associated with both independent and dependent quantities. Applications also include those to Kleinian groups and rational maps. Compared to previous works our framework allows us to successfully remove many unnecessary conditions and strengthen fundamental results such as Jarník's theorem and the Baker-Schmidt theorem. In particular, the strengthening of Jarník's theorem opens up the Duffin-Schaeffer conjecturefor Hausdorff measures.
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
