Vertex Algebras and Geometry, Thomas Creutzig, Andrew R. Linshaw
Автор: Xiaoping Xu Название: Introduction to Vertex Operator Superalgebras and Their Modules ISBN: 0792352424 ISBN-13(EAN): 9780792352426 Издательство: Springer Рейтинг: Цена: 102480.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Presents a study on the structures of vertex operator superalgebras and their modules. This book includes related theories of self-dual codes and lattices, as well as achievements on classifications of certain simple vertex operator superalgebras and their irreducible twisted modules.
Автор: Alexander Molev Название: Sugawara Operators for Classical Lie Algebras ISBN: 1470436590 ISBN-13(EAN): 9781470436599 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 107850.00 T Наличие на складе: Невозможна поставка. Описание: The celebrated Schur-Weyl duality gives rise to effective ways of constructing invariant polynomials on the classical Lie algebras. The emergence of the theory of quantum groups in the 1980s brought up special matrix techniques which allowed one to extend these constructions beyond polynomial invariants and produce new families of Casimir elements for finite-dimensional Lie algebras. Sugawara operators are analogs of Casimir elements for the affine Kac-Moody algebras.The goal of this book is to describe algebraic structures associated with the affine Lie algebras, including affine vertex algebras, Yangians, and classical $\mathcal{W}$-algebras, which have numerous ties with many areas of mathematics and mathematical physics, including modular forms, conformal field theory, and soliton equations. An affine version of the matrix technique is developed and used to explain the elegant constructions of Sugawara operators, which appeared in the last decade. An affine analogue of the Harish-Chandra isomorphism connects the Sugawara operators with the classical $\mathcal{W}$-algebras, which play the role of the Weyl group invariants in the finite-dimensional theory.
Автор: Frenkel E., Ben-Zwi D. Название: Vertex algebras and algebraic curves ISBN: 0821836749 ISBN-13(EAN): 9780821836743 Издательство: Неизвестно Рейтинг: Цена: 139330.00 T Наличие на складе: Невозможна поставка. Описание: Presents an introduction to the theory of vertex algebras with a particular emphasis on the relationship with the geometry of algebraic curves. This book contains several topics, in particular an introduction to the Beilinson-Drinfeld theory of factorization algebras and the geometric Langlands correspondence.
Автор: Katrina Barron, Elizabeth Jurisich, Antun Milas, Kailash Misra Название: Lie Algebras, Vertex Operator Algebras, and Related Topics ISBN: 1470426668 ISBN-13(EAN): 9781470426668 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 110880.00 T Наличие на складе: Невозможна поставка. Описание: Contains the proceedings of the conference on Lie Algebras, Vertex Operator Algebras, and Related Topics, celebrating the 70th birthday of James Lepowsky and Robert Wilson. The papers presented here include recent results and descriptions of ongoing research initiatives representing the broad influence and deep connections brought about by the work of Lepowsky and Wilson.
Автор: Hirotaka Tamanoi Название: Elliptic Genera and Vertex Operator Super-Algebras ISBN: 3540660062 ISBN-13(EAN): 9783540660064 Издательство: Springer Рейтинг: Цена: 46540.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This monograph deals with two aspects of the theory of elliptic genus: its topological aspect involving elliptic functions, and its representation theoretic aspect involving vertex operator super-algebras.
Автор: Xiaoping Xu Название: Introduction to Vertex Operator Superalgebras and Their Modules ISBN: 9048150965 ISBN-13(EAN): 9789048150960 Издательство: Springer Рейтинг: Цена: 181630.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Vertex algebra was introduced by Boreherds, and the slightly revised notion "vertex oper- ator algebra" was formulated by Frenkel, Lepowsky and Meurman, in order to solve the problem of the moonshine representation of the Monster group - the largest sporadie group. On the one hand, vertex operator algebras ean be viewed as extensions of eertain infinite-dimensional Lie algebras such as affine Lie algebras and the Virasoro algebra. On the other hand, they are natural one-variable generalizations of commutative associative algebras with an identity element. In a certain sense, Lie algebras and commutative asso- ciative algebras are reconciled in vertex operator algebras. Moreover, some other algebraie structures, such as integral linear lattiees, Jordan algebras and noncommutative associa- tive algebras, also appear as subalgebraic structures of vertex operator algebras. The axioms of vertex operator algebra have geometrie interpretations in terms of Riemman spheres with punctures. The trace functions of a certain component of vertex operators enjoy the modular invariant properties. Vertex operator algebras appeared in physies as the fundamental algebraic structures of eonformal field theory, whieh plays an important role in string theory and statistieal meehanies. Moreover, eonformalfieldtheoryreveals animportantmathematiealproperty, the so called "mirror symmetry" among Calabi-Yau manifolds. The general correspondence between vertex operator algebras and Calabi-Yau manifolds still remains mysterious. Ever since the first book on vertex operator algebras by Frenkel, Lepowsky and Meur- man was published in 1988, there has been a rapid development in vertex operator su- peralgebras, which are slight generalizations of vertex operator algebras.
Автор: Alex Martsinkovsky, Kiyoshi Igusa, Gordana Todorov Название: Surveys in Representation Theory of Algebras ISBN: 1470436795 ISBN-13(EAN): 9781470436797 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 116430.00 T Наличие на складе: Невозможна поставка. Описание: Contains selected expository lectures delivered at the annual Maurice Auslander Distinguished Lectures and International Conference over the last several years. The selected articles reflect the diverse landscape of modern representation theory of algebras.
This unique book's subject is meanders (connected, oriented, non-self-intersecting planar curves intersecting the horizontal line transversely) in the context of dynamical systems. By interpreting the transverse intersection points as vertices and the arches arising from these curves as directed edges, meanders are introduced from the graphtheoretical perspective. Supplementing the rigorous results, mathematical methods, constructions, and examples of meanders with a large number of insightful figures, issues such as connectivity and the number of connected components of meanders are studied in detail with the aid of collapse and multiple collapse, forks, and chambers. Moreover, the author introduces a large class of Morse meanders by utilizing the right and left one-shift maps, and presents connections to Sturm global attractors, seaweed and Frobenius Lie algebras, and the classical Yang-Baxter equation.
Contents
Seaweed Meanders
Meanders
Morse Meanders and Sturm Global Attractors
Right and Left One-Shifts
Connection Graphs of Type I, II, III and IV
Meanders and the Temperley-Lieb Algebra
Representations of Seaweed Lie Algebras
CYBE and Seaweed Meanders
Автор: Gille, Philippe Szamuely, Tamas Название: Central simple algebras and galois cohomology ISBN: 131660988X ISBN-13(EAN): 9781316609880 Издательство: Cambridge Academ Рейтинг: Цена: 47520.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The first comprehensive, modern introduction to a central field in modern algebra with connections to algebraic geometry, K-theory, and number theory. It proceeds from the basics to more advanced results, including the Merkurjev-Suslin theorem. It is ideal as a text for a graduate course and as a reference for researchers.
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