Elliptic Genera And Vertex Operator Super Algebras
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Author | : Hirotaka Tamanoi |
Publisher | : Springer |
Total Pages | : 397 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540487883 |
Download Elliptic Genera and Vertex Operator Super-Algebras Book in PDF, Epub and Kindle
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. For the second aspect, elliptic genera are shown to have the structure of modules over certain vertex operator super-algebras. The vertex operators corresponding to parallel tensor fields on closed Riemannian Spin Kähler manifolds such as Riemannian tensors and Kähler forms are shown to give rise to Virasoro algebras and affine Lie algebras. This monograph is chiefly intended for topologists and it includes accounts on topics outside of topology such as vertex operator algebras.
Author | : Chongying Dong |
Publisher | : Springer Science & Business Media |
Total Pages | : 207 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461203538 |
Download Generalized Vertex Algebras and Relative Vertex Operators Book in PDF, Epub and Kindle
The rapidly-evolving theory of vertex operator algebras provides deep insight into many important algebraic structures. Vertex operator algebras can be viewed as "complex analogues" of both Lie algebras and associative algebras. The monograph is written in a n accessible and self-contained manner, with detailed proofs and with many examples interwoven through the axiomatic treatment as motivation and applications. It will be useful for research mathematicians and theoretical physicists working the such fields as representation theory and algebraic structure sand will provide the basis for a number of graduate courses and seminars on these and related topics.
Author | : Xiaoping Xu |
Publisher | : Springer Science & Business Media |
Total Pages | : 371 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 9401590974 |
Download Introduction to Vertex Operator Superalgebras and Their Modules Book in PDF, Epub and Kindle
This book presents a systematic study on the structures of vertex operator superalgebras and their modules. Related theories of self-dual codes and lattices are included, as well as recent achievements on classifications of certain simple vertex operator superalgebras and their irreducible twisted modules, constructions of simple vertex operator superalgebras from graded associative algebras and their anti-involutions, self-dual codes and lattices. Audience: This book is of interest to researchers and graduate students in mathematics and mathematical physics.
Author | : Hirotaka Tamanoi |
Publisher | : Springer |
Total Pages | : 396 |
Release | : 1999-06-21 |
Genre | : Mathematics |
ISBN | : 9783540660064 |
Download Elliptic Genera and Vertex Operator Super-Algebras Book in PDF, Epub and Kindle
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. For the second aspect, elliptic genera are shown to have the structure of modules over certain vertex operator super-algebras. The vertex operators corresponding to parallel tensor fields on closed Riemannian Spin Kähler manifolds such as Riemannian tensors and Kähler forms are shown to give rise to Virasoro algebras and affine Lie algebras. This monograph is chiefly intended for topologists and it includes accounts on topics outside of topology such as vertex operator algebras.
Author | : James Lepowsky |
Publisher | : Springer Science & Business Media |
Total Pages | : 330 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 0817681868 |
Download Introduction to Vertex Operator Algebras and Their Representations Book in PDF, Epub and Kindle
* Introduces the fundamental theory of vertex operator algebras and its basic techniques and examples. * Begins with a detailed presentation of the theoretical foundations and proceeds to a range of applications. * Includes a number of new, original results and brings fresh perspective to important works of many other researchers in algebra, lie theory, representation theory, string theory, quantum field theory, and other areas of math and physics.
Author | : Stephen Berman |
Publisher | : American Mathematical Soc. |
Total Pages | : 268 |
Release | : |
Genre | : Mathematics |
ISBN | : 9780821871447 |
Download Vertex Operator Algebras in Mathematics and Physics Book in PDF, Epub and Kindle
Vertex operator algebras are a class of algebras underlying a number of recent constructions, results, and themes in mathematics. These algebras can be understood as ''string-theoretic analogues'' of Lie algebras and of commutative associative algebras. They play fundamental roles in some of the most active research areas in mathematics and physics. Much recent progress in both physics and mathematics has benefited from cross-pollination between the physical and mathematical points of view. This book presents the proceedings from the workshop, ''Vertex Operator Algebras in Mathematics and Physics'', held at The Fields Institute. It consists of papers based on many of the talks given at the conference by leading experts in the algebraic, geometric, and physical aspects of vertex operator algebra theory. The book is suitable for graduate students and research mathematicians interested in the major themes and important developments on the frontier of research in vertex operator algebra theory and its applications in mathematics and physics.
Author | : Igor Frenkel |
Publisher | : Academic Press |
Total Pages | : 563 |
Release | : 1989-05-01 |
Genre | : Mathematics |
ISBN | : 0080874541 |
Download Vertex Operator Algebras and the Monster Book in PDF, Epub and Kindle
This work is motivated by and develops connections between several branches of mathematics and physics--the theories of Lie algebras, finite groups and modular functions in mathematics, and string theory in physics. The first part of the book presents a new mathematical theory of vertex operator algebras, the algebraic counterpart of two-dimensional holomorphic conformal quantum field theory. The remaining part constructs the Monster finite simple group as the automorphism group of a very special vertex operator algebra, called the "moonshine module" because of its relevance to "monstrous moonshine."
Author | : Nihon Gakushiin |
Publisher | : |
Total Pages | : 324 |
Release | : 1995 |
Genre | : Mathematics |
ISBN | : |
Download Proceedings of the Japan Academy Book in PDF, Epub and Kindle
Author | : John McKay |
Publisher | : American Mathematical Soc. |
Total Pages | : 280 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : 0821828797 |
Download Proceedings on Moonshine and Related Topics Book in PDF, Epub and Kindle
This volume contains the proceedings of the Moonshine workshop held at the Centre de Recherches Mathematiques (CRM) in Montreal. In this volume, all the classical Moonshine themes are presented, namely the Monster simple group and other finite groups, automorphic functions and forms and related congruence groups, and vertex algebras and their representations. These topics appear in either a pure form or in a blend of algebraic geometry dealing with algebraic surfaces, Picard-Fuchsequations, and hypergeometric functions.
Author | : Yi-Zhi Huang |
Publisher | : Springer Science & Business Media |
Total Pages | : 289 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461242762 |
Download Two-Dimensional Conformal Geometry and Vertex Operator Algebras Book in PDF, Epub and Kindle
The theory of vertex operator algebras and their representations has been showing its power in the solution of concrete mathematical problems and in the understanding of conceptual but subtle mathematical and physical struc- tures of conformal field theories. Much of the recent progress has deep connec- tions with complex analysis and conformal geometry. Future developments, especially constructions and studies of higher-genus theories, will need a solid geometric theory of vertex operator algebras. Back in 1986, Manin already observed in Man) that the quantum theory of (super )strings existed (in some sense) in two entirely different mathematical fields. Under canonical quantization this theory appeared to a mathematician as the representation theories of the Heisenberg, Vir as oro and affine Kac- Moody algebras and their superextensions. Quantization with the help of the Polyakov path integral led on the other hand to the analytic theory of algebraic (super ) curves and their moduli spaces, to invariants of the type of the analytic curvature, and so on.He pointed out further that establishing direct mathematical connections between these two forms of a single theory was a big and important problem. On the one hand, the theory of vertex operator algebras and their repre- sentations unifies (and considerably extends) the representation theories of the Heisenberg, Virasoro and Kac-Moody algebras and their superextensions.