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Projective Modules Over Lie Algebras Of Cartan Type
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Book Synopsis Projective Modules over Lie Algebras of Cartan Type by : Daniel Ken Nakano
Download or read book Projective Modules over Lie Algebras of Cartan Type written by Daniel Ken Nakano and published by American Mathematical Soc.. This book was released on 1992 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph focuses on extending theorems for the classical Lie algebras in order to determine the structure and representation theory for Lie algebras of Cartan type. More specifically, Nakano investigates the block theory for the restricted universal enveloping algebras of the Lie algebras of Cartan type. The first section employs techniques developed by Holmes and Nakano to prove a Brauer-Humphreys reciprocity law for graded restricted Lie algebras and also to find the decompositions for the intermediate (Verma) modules used in the reciprocity law. The second section uses this information to investigate the structure of projective modules for the Lie algebras of types W and K. The restricted enveloping algebras for these Lie algebras are shown to have one block. Furthermore, Nakano provides a procedure for computing the Cartan invariants for Lie algebras of types W and K, given knowledge about the decomposition of the generalized Verma modules and about the Jantzen matrix of the classical/reductive zero component. Noteworthy for its readability and the continuity of its theme and purpose, this monograph appeals to graduate students and researchers interested in Lie algebras.
Book Synopsis Modular Lie Algebras and their Representations by : H. Strade
Download or read book Modular Lie Algebras and their Representations written by H. Strade and published by CRC Press. This book was released on 2020-08-11 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an introduction to the structure and representation theory of modular Lie algebras over fields of positive characteristic. It introduces the beginner to the theory of modular Lie algebras and is meant to be a reference text for researchers.
Book Synopsis The Monster and Lie Algebras by : Joseph Ferrar
Download or read book The Monster and Lie Algebras written by Joseph Ferrar and published by Walter de Gruyter. This book was released on 2011-06-24 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thisseries is devoted to the publication of monographs, lecture resp. seminar notes, and other materials arising from programs of the OSU Mathemaical Research Institute. This includes proceedings of conferences or workshops held at the Institute, and other mathematical writings.
Book Synopsis Lie Algebras and Related Topics by : Daniel J. Britten
Download or read book Lie Algebras and Related Topics written by Daniel J. Britten and published by American Mathematical Soc.. This book was released on 1986 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the Proceedings of the 1984 Canadian Mathematical Society's Summer Seminar, this book focuses on some advances in the theory of semisimple Lie algebras and some direct outgrowths of that theory. The following papers are of particular interest: an important survey article by R. Block and R. Wilson on restricted simple Lie algebras, a survey of universal enveloping algebras of semisimple Lie algebras by W. Borho, a course on Kac-Moody Lie algebras by I. G. Macdonald with an extensive bibliography of this field by Georgia Benkart, and a course on formal groups by M. Hazewinkel. Because of the expository surveys and courses, the book will be especially useful to graduate students in Lie theory, as well as to researchers in the field.
Book Synopsis Constructions of Lie Algebras and their Modules by : George B. Seligman
Download or read book Constructions of Lie Algebras and their Modules written by George B. Seligman and published by Springer. This book was released on 2006-11-14 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with central simple Lie algebras over arbitrary fields of characteristic zero. It aims to give constructions of the algebras and their finite-dimensional modules in terms that are rational with respect to the given ground field. All isotropic algebras with non-reduced relative root systems are treated, along with classical anisotropic algebras. The latter are treated by what seems to be a novel device, namely by studying certain modules for isotropic classical algebras in which they are embedded. In this development, symmetric powers of central simple associative algebras, along with generalized even Clifford algebras of involutorial algebras, play central roles. Considerable attention is given to exceptional algebras. The pace is that of a rather expansive research monograph. The reader who has at hand a standard introductory text on Lie algebras, such as Jacobson or Humphreys, should be in a position to understand the results. More technical matters arise in some of the detailed arguments. The book is intended for researchers and students of algebraic Lie theory, as well as for other researchers who are seeking explicit realizations of algebras or modules. It will probably be more useful as a resource to be dipped into, than as a text to be worked straight through.
Book Synopsis Lie Algebras and Related Topics by : Marina Avitabile
Download or read book Lie Algebras and Related Topics written by Marina Avitabile and published by American Mathematical Soc.. This book was released on 2015-11-30 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Workshop on Lie Algebras, in honor of Helmut Strade's 70th Birthday, held from May 22-24, 2013, at the Università degli Studi di Milano-Bicocca, Milano, Italy. Lie algebras are at the core of several areas of mathematics, such as, Lie groups, algebraic groups, quantum groups, representation theory, homogeneous spaces, integrable systems, and algebraic topology. The first part of this volume combines research papers with survey papers by the invited speakers. The second part consists of several collections of problems on modular Lie algebras, their representations, and the conjugacy of their nilpotent elements as well as the Koszulity of (restricted) Lie algebras and Lie properties of group algebras or restricted universal enveloping algebras.
Book Synopsis Abstract Lie Algebras by : David J Winter
Download or read book Abstract Lie Algebras written by David J Winter and published by Courier Corporation. This book was released on 2013-12-01 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solid but concise, this account of Lie algebra emphasizes the theory's simplicity and offers new approaches to major theorems. Author David J. Winter, a Professor of Mathematics at the University of Michigan, also presents a general, extensive treatment of Cartan and related Lie subalgebras over arbitrary fields. Preliminary material covers modules and nonassociate algebras, followed by a compact, self-contained development of the theory of Lie algebras of characteristic 0. Topics include solvable and nilpotent Lie algebras, Cartan subalgebras, and Levi's radical splitting theorem and the complete reducibility of representations of semisimple Lie algebras. Additional subjects include the isomorphism theorem for semisimple Lie algebras and their irreducible modules, automorphism of Lie algebras, and the conjugacy of Cartan subalgebras and Borel subalgebras. An extensive theory of Cartan and related subalgebras of Lie algebras over arbitrary fields is developed in the final chapter, and an appendix offers background on the Zariski topology.
Book Synopsis Representation Theory by : Zongzhu Lin
Download or read book Representation Theory written by Zongzhu Lin and published by American Mathematical Soc.. This book was released on 2009-01-16 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nothing provided
Book Synopsis Lie Algebras and Related Topics by : Georgia Benkart
Download or read book Lie Algebras and Related Topics written by Georgia Benkart and published by American Mathematical Soc.. This book was released on 1990 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 1984 classification of the finite-dimensional restricted simple Lie algebras over an algebraically closed field of characteristic $p>7$ provided the impetus for a Special Year of Lie Algebras, held at the University of Wisconsin, Madison, during 1987-88. Work done during the Special Year and afterward put researchers much closer toward a solution of the long-standing problem of determining the finite-dimensional simple Lie algebras over an algebraically closed field of characteristic $p>7$. This volume contains the proceedings of a conference on Lie algebras and related topics, held in May 1988 to mark the end of the Special Year. The conference featured lectures on Lie algebras of prime characteristic, algebraic groups, combinatorics and representation theory, and Kac-Moody and Virasoro algebras. Many facets of recent research on Lie theory are reflected in the papers presented here, testifying to the richness and diversity of this topic.
Book Synopsis Non-Associative Algebra and Its Applications by : Santos González
Download or read book Non-Associative Algebra and Its Applications written by Santos González and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Third International Conference on Non-Associative Algebra and Its Applications, held in Oviedo, Spain, July 12--17, 1993. The conference brought together specialists from all over the world who work in this interesting and active field, which is currently enjoying much attention. All aspects of non-associative algebra are covered. Topics range from purely mathematical subjects to a wide spectrum of applications, and from state-of-the-art articles to overview papers. This collection will point the way for further research for many years to come. The volume is of interest to researchers in mathematics as well as those whose work involves the application of non-associative algebra in such areas as physics, biology and genetics.
Book Synopsis Categories of Modules over Endomorphism Rings by : Theodore Gerard Faticoni
Download or read book Categories of Modules over Endomorphism Rings written by Theodore Gerard Faticoni and published by American Mathematical Soc.. This book was released on 1993 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is the goal of the memoir to develop a functorial transfer of properties between [italic capital]A and [script capital]M[subscript italic capital]E, the category of modules over [italic capital]E, that is more sensitive than the traditional starting point, Hom([italic capital]A, ·). This memoir should be accessible to anyone who has a working knowledge of rings, modules, functors, and categories equivalent to that gained by reading Anderson and Fuller's text "Rings and Categories of Modules."
Download or read book Lie Algebras written by Nathan Jacobson and published by Courier Corporation. This book was released on 2013-09-16 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: DIVDefinitive treatment of important subject in modern mathematics. Covers split semi-simple Lie algebras, universal enveloping algebras, classification of irreducible modules, automorphisms, simple Lie algebras over an arbitrary field, etc. Index. /div
Book Synopsis Invariant Subsemigroups of Lie Groups by : Karl-Hermann Neeb
Download or read book Invariant Subsemigroups of Lie Groups written by Karl-Hermann Neeb and published by American Mathematical Soc.. This book was released on 1993 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents the first systematic treatment of invariant Lie semi groups. Because these semi groups provide interesting models for space times in general relativity, this work will be useful to both mathematicians and physicists. It will also appeal to engineers interested in bi-invariant control systems on Lie groups. Neeb investigates closed invariant subsemigroups of Lie groups which are generated by one-parameter semi groups and the sets of infinitesimal generators of such semi groups - invariant convex cones in Lie algebras.In addition, a characterization of those finite-dimensional real Lie algebras containing such cones is obtained. The global part of the theory deals with globality problems (Lie's third theorem for semi groups), controllability problems, and the facial structure of Lie semi groups. Neeb also determines the structure of the universal compactification of an invariant Lie semigroup and shows that the lattice of idempotents is isomorphic to a lattice of faces of the cone dual to the cone of infinitesimal generators.
Book Synopsis On Axiomatic Approaches to Vertex Operator Algebras and Modules by : Igor Frenkel
Download or read book On Axiomatic Approaches to Vertex Operator Algebras and Modules written by Igor Frenkel and published by American Mathematical Soc.. This book was released on 1993 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of vertex operator algebra arises naturally in the vertex operator construction of the Monster - the largest sporadic finite simple group. From another perspective, the theory of vertex operator algebras and their modules forms the algebraic foundation of conformal field theory. Vertex operator algebras and conformal field theory are now known to be deeply related to many important areas of mathematics. This essentially self-contained monograph develops the basic axiomatic theory of vertex operator algebras and their modules and intertwining operators, following a fundamental analogy with Lie algebra theory. The main axiom, the 'Jacobi(-Cauchy) identity', is a far-reaching analog of the Jacobi identity for Lie algebras.The authors show that the Jacobi identity is equivalent to suitably formulated rationality, commutativity, and associativity properties of products of quantum fields. A number of other foundational and useful results are also developed. This work was originally distributed as a preprint in 1989, and in view of the current widespread interest in the subject among mathematicians and theoretical physicists, its publication and availability should prove no less useful than when it was written.
Book Synopsis Littlewood-Paley Theory on Spaces of Homogeneous Type and the Classical Function Spaces by : Yongsheng Han
Download or read book Littlewood-Paley Theory on Spaces of Homogeneous Type and the Classical Function Spaces written by Yongsheng Han and published by American Mathematical Soc.. This book was released on 1994 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work, Han and Sawyer extend Littlewood-Paley theory, Besov spaces, and Triebel-Lizorkin spaces to the general setting of a space of homogeneous type. For this purpose, they establish a suitable analogue of the Calder 'on reproducing formula and use it to extend classical results on atomic decomposition, interpolation, and T1 and Tb theorems. Some new results in the classical setting are also obtained: atomic decompositions with vanishing b-moment, and Littlewood-Paley characterizations of Besov and Triebel-Lizorkin spaces with only half the usual smoothness and cancellation conditions on the approximate identity.
Book Synopsis Rational Constructions of Modules for Simple Lie Algebras by : George B. Seligman
Download or read book Rational Constructions of Modules for Simple Lie Algebras written by George B. Seligman and published by American Mathematical Soc.. This book was released on 1981 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is directed to researchers in Lie theory and in the theory of linear algebra, associative or otherwise, and to graduate students who have had some background in one or more of these areas.
Book Synopsis Theory and Applications of Holomorphic Functions on Algebraic Varieties over Arbitrary Ground Fields by : Oscar Zariski
Download or read book Theory and Applications of Holomorphic Functions on Algebraic Varieties over Arbitrary Ground Fields written by Oscar Zariski and published by American Mathematical Soc.. This book was released on 1951 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt:
