[PDF] Algebraic Structures And Their Representations eBook

Author : José Antonio de la Peña
Publisher : American Mathematical Soc.
Page : 466 pages
File Size : 16,40 MB
Release : 2005
Category : Mathematics
ISBN : 0821836307

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The Latin-American conference on algebra, the XV Coloquio Latinoamericano de Algebra (Cocoyoc, Mexico), consisted of plenary sessions of general interest and special sessions on algebraic combinatorics, associative rings, cohomology of rings and algebras, commutative algebra, group representations, Hopf algebras, number theory, quantum groups, and representation theory of algebras. This proceedings volume contains original research papers related to talks at the colloquium. In addition, there are several surveys presenting important topics to a broad mathematical audience. There are also two invited papers by Raymundo Bautista and Roberto Martinez, founders of the Mexican school of representation theory of algebras. The book is suitable for graduate students and researchers interested in algebra.

Author : Joseph Landin
Publisher : Courier Corporation
Page : 275 pages
File Size : 34,74 MB
Release : 2012-08-29
Category : Mathematics
ISBN : 0486150410

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This self-contained text covers sets and numbers, elements of set theory, real numbers, the theory of groups, group isomorphism and homomorphism, theory of rings, and polynomial rings. 1969 edition.

Author : Palash B. Pal
Publisher : Cambridge University Press
Page : 717 pages
File Size : 40,10 MB
Release : 2019-05-23
Category : Science
ISBN : 1108492207

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Algebraic structures including vector space, groups, topological spaces and more, all covered in one volume, showing the mutual connections.

Author : Mahouton Norbert Hounkonnou
Publisher : Springer Nature
Page : 600 pages
File Size : 40,90 MB
Release : 2023-12-01
Category : Mathematics
ISBN : 3031393341

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This book gathers invited, peer-reviewed works presented at the 2021 edition of the Classical and Constructive Nonassociative Algebraic Structures: Foundations and Applications—CaCNAS: FA 2021, virtually held from June 30 to July 2, 2021, in dedication to the memory of Professor Nebojša Stevanović (1962-2009). The papers cover new trends in the field, focusing on the growing development of applications in other disciplines. These aspects interplay in the same cadence, promoting interactions between theory and applications, and between nonassociative algebraic structures and various fields in pure and applied mathematics. In this volume, the reader will find novel studies on topics such as left almost algebras, logical algebras, groupoids and their generalizations, algebraic geometry and its relations with quiver algebras, enumerative combinatorics, representation theory, fuzzy logic and foundation theory, fuzzy algebraic structures, group amalgams, computer-aided development and transformation of the theory of nonassociative algebraic structures, and applications within natural sciences and engineering. Researchers and graduate students in algebraic structures and their applications can hugely benefit from this book, which can also interest any researcher exploring multi-disciplinarity and complexity in the scientific realm.

Author : Leonid Positselski
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 14,14 MB
Release : 2010-09-02
Category : Mathematics
ISBN : 303460436X

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This book provides comprehensive coverage on semi-infinite homology and cohomology of associative algebraic structures. It features rich representation-theoretic and algebro-geometric examples and applications.

Author : Alex J. Feingold
Publisher : American Mathematical Soc.
Page : 158 pages
File Size : 34,85 MB
Release : 1991
Category : Mathematics
ISBN : 0821851284

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The theory of vertex operator algebras is a remarkably rich new mathematical field which captures the algebraic content of conformal field theory in physics. Ideas leading up to this theory appeared in physics as part of statistical mechanics and string theory. In mathematics, the axiomatic definitions crystallized in the work of Borcherds and in Vertex Operator Algebras and the Monster, by Frenkel, Lepowsky, and Meurman. The structure of monodromies of intertwining operators for modules of vertex operator algebras yield braid group representations and leads to natural generalizations of vertex operator algebras, such as superalgebras and para-algebras. Many examples of vertex operator algebras and their generalizations are related to constructions in classical representation theory and shed new light on the classical theory. This book accomplishes several goals. The authors provide an explicit spinor construction, using only Clifford algebras, of a vertex operator superalgebra structure on the direct sum of the basic and vector modules for the affine Kac-Moody algebra Dn(1). They also review and extend Chevalley's spinor construction of the 24-dimensional commutative nonassociative algebraic structure and triality on the direct sum of the three 8-dimensional D4-modules. Vertex operator para-algebras, introduced and developed independently in this book and by Dong and Lepowsky, are related to one-dimensional representations of the braid group. The authors also provide a unified approach to the Chevalley, Greiss, and E8 algebras and explain some of their similarities. A Third goal is to provide a purely spinor construction of the exceptional affine Lie algebra E8(1), a natural continuation of previous work on spinor and oscillator constructions of the classical affine Lie algebras. These constructions should easily extend to include the rest of the exceptional affine Lie algebras. The final objective is to develop an inductive technique of construction which could be applied to the Monster vertex operator algebra. Directed at mathematicians and physicists, this book should be accessible to graduate students with some background in finite-dimensional Lie algebras and their representations. Although some experience with affine Kac-Moody algebras would be useful, a summary of the relevant parts of that theory is included. This book shows how the concepts and techniques of Lie theory can be generalized to yield the algebraic structures associated with conformal field theory. The careful reader will also gain a detailed knowledge of how the spinor construction of classical triality lifts to the affine algebras and plays an important role in the spinor construction of vertex operator algebras, modules, and intertwining operators with nontrivial monodromies.

Author : P. Feinsilver
Publisher : Springer Science & Business Media
Page : 246 pages
File Size : 45,6 MB
Release : 1993
Category : Computers
ISBN : 9780792338345

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Introduction I. General remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 II. Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 III. Lie algebras: some basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Chapter 1 Operator calculus and Appell systems I. Boson calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 II. Holomorphic canonical calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 III. Canonical Appell systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Chapter 2 Representations of Lie groups I. Coordinates on Lie groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 II. Dual representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 III. Matrix elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 IV. Induced representations and homogeneous spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 General Appell systems Chapter 3 I. Convolution and stochastic processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 II. Stochastic processes on Lie groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 III. Appell systems on Lie groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Chapter 4 Canonical systems in several variables I. Homogeneous spaces and Cartan decompositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 II. Induced representation and coherent states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 III. Orthogonal polynomials in several variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Chapter 5 Algebras with discrete spectrum I. Calculus on groups: review of the theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 II. Finite-difference algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 III. q-HW algebra and basic hypergeometric functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 IV. su2 and Krawtchouk polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 V. e2 and Lommel polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Chapter 6 Nilpotent and solvable algebras I. Heisenberg algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 II. Type-H Lie algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 Vll III. Upper-triangular matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 IV. Affine and Euclidean algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Chapter 7 Hermitian symmetric spaces I. Basic structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 II. Space of rectangular matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 III. Space of skew-symmetric matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 IV. Space of symmetric matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Chapter 8 Properties of matrix elements I. Addition formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 II. Recurrences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 III. Quotient representations and summation formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 Chapter 9 Symbolic computations I. Computing the pi-matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 II. Adjoint group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 III. Recursive computation of matrix elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Author : Jens Carsten Jantzen
Publisher : American Mathematical Soc.
Page : 594 pages
File Size : 15,11 MB
Release : 2003
Category : Mathematics
ISBN : 082184377X

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Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.

Author : Ibrahim Assem
Publisher : American Mathematical Soc.
Page : 257 pages
File Size : 39,55 MB
Release : 2021-01-06
Category : Education
ISBN : 147045159X

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The Seventh ARTA (“Advances in Representation Theory of Algebras VII”) conference took place at the Instituto de Matemáticas of the Universidad Nacional Autónoma de México, in Mexico City, from September 24–28, 2018, in honor of José Antonio de la Peña's 60th birthday. Papers in this volume cover topics Professor de la Peña worked on, such as covering theory, tame algebras, and the use of quadratic forms in representation theory. Also included are papers on the categorical approach to representations of algebras and relations to Lie theory, Cohen–Macaulay modules, quantum groups and other algebraic structures.