Classical Lie Algebras At Infinity
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Classical Lie Algebras At Infinity
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Author : Ivan Penkov
language : en
Publisher: Springer Nature
Release Date : 2022-01-05
Classical Lie Algebras At Infinity written by Ivan Penkov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-05 with Mathematics categories.
Originating from graduate topics courses given by the first author, this book functions as a unique text-monograph hybrid that bridges a traditional graduate course to research level representation theory. The exposition includes an introduction to the subject, some highlights of the theory and recent results in the field, and is therefore appropriate for advanced graduate students entering the field as well as research mathematicians wishing to expand their knowledge. The mathematical background required varies from chapter to chapter, but a standard course on Lie algebras and their representations, along with some knowledge of homological algebra, is necessary. Basic algebraic geometry and sheaf cohomology are needed for Chapter 10. Exercises of various levels of difficulty are interlaced throughout the text to add depth to topical comprehension. The unifying theme of this book is the structure and representation theory of infinite-dimensional locally reductive Lie algebras and superalgebras. Chapters 1-6 are foundational; each of the last 4 chapters presents a self-contained study of a specialized topic within the larger field. Lie superalgebras and flag supermanifolds are discussed in Chapters 3, 7, and 10, and may be skipped by the reader.
Stability In Modules For Classical Lie Algebras A Constructive Approach
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Author : Georgia Benkart
language : en
Publisher: American Mathematical Soc.
Release Date : 1990
Stability In Modules For Classical Lie Algebras A Constructive Approach written by Georgia Benkart and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
In this work we consider the problem of determining information about representations as the rank grows large, in fact, tends to infinity. Here we show that the set of dominant weights stabilizes as the rank goes to infinity and the multiplicities become polynomials in the rank. In addition, we give effective, easily computable algorithms for determining the set of dominant weights and illustrate how to calculate their multiplicity polynomials.
Advances In Lie Superalgebras
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Author : Maria Gorelik
language : en
Publisher: Springer Science & Business
Release Date : 2014-04-28
Advances In Lie Superalgebras written by Maria Gorelik and has been published by Springer Science & Business this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-28 with Mathematics categories.
The volume is the outcome of the conference "Lie superalgebras," which was held at the Istituto Nazionale di Alta Matematica, in 2012. The conference gathered many specialists in the subject, and the talks held provided comprehensive insights into the newest trends in research on Lie superalgebras (and related topics like vertex algebras, representation theory and supergeometry). The book contains contributions of many leading esperts in the field and provides a complete account of the newest trends in research on Lie Superalgebras.
Perspectives In Lie Theory
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Author : Filippo Callegaro
language : en
Publisher: Springer
Release Date : 2017-12-07
Perspectives In Lie Theory written by Filippo Callegaro and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-07 with Mathematics categories.
Lie theory is a mathematical framework for encoding the concept of symmetries of a problem, and was the central theme of an INdAM intensive research period at the Centro de Giorgi in Pisa, Italy, in the academic year 2014-2015. This book gathers the key outcomes of this period, addressing topics such as: structure and representation theory of vertex algebras, Lie algebras and superalgebras, as well as hyperplane arrangements with different approaches, ranging from geometry and topology to combinatorics.
Connected At Infinity Ii A Selection Of Mathematics By Indians
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Author : Rajendra Bhatia
language : en
Publisher: Springer
Release Date : 2013-01-01
Connected At Infinity Ii A Selection Of Mathematics By Indians written by Rajendra Bhatia and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-01 with Mathematics categories.
Semi Simple Lie Algebras And Their Representations
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Author : Robert N. Cahn
language : en
Publisher: Courier Corporation
Release Date : 2014-06-10
Semi Simple Lie Algebras And Their Representations written by Robert N. Cahn and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-10 with Mathematics categories.
Designed to acquaint students of particle physiME already familiar with SU(2) and SU(3) with techniques applicable to all simple Lie algebras, this text is especially suited to the study of grand unification theories. Author Robert N. Cahn, who is affiliated with the Lawrence Berkeley National Laboratory in Berkeley, California, has provided a new preface for this edition. Subjects include the killing form, the structure of simple Lie algebras and their representations, simple roots and the Cartan matrix, the classical Lie algebras, and the exceptional Lie algebras. Additional topiME include Casimir operators and Freudenthal's formula, the Weyl group, Weyl's dimension formula, reducing product representations, subalgebras, and branching rules. 1984 edition.
Affine Lie Algebras And Quantum Groups
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Author : Jürgen Fuchs
language : en
Publisher: Cambridge University Press
Release Date : 1995-03-09
Affine Lie Algebras And Quantum Groups written by Jürgen Fuchs and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-03-09 with Mathematics categories.
This is an introduction to the theory of affine Lie Algebras, to the theory of quantum groups, and to the interrelationships between these two fields that are encountered in conformal field theory.
Yang Baxter Equation In Integrable Systems
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Author : Michio Jimbo
language : ja
Publisher: World Scientific
Release Date : 1990
Yang Baxter Equation In Integrable Systems written by Michio Jimbo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Science categories.
This volume will be the first reference book devoted specially to the Yang-Baxter equation. The subject relates to broad areas including solvable models in statistical mechanics, factorized S matrices, quantum inverse scattering method, quantum groups, knot theory and conformal field theory. The articles assembled here cover major works from the pioneering papers to classical Yang-Baxter equation, its quantization, variety of solutions, constructions and recent generalizations to higher genus solutions.
Advances In Quantum Computation
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Author : Kazem Mahdavi
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-04-01
Advances In Quantum Computation written by Kazem Mahdavi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-01 with Mathematics categories.
This volume represents the talks given at the Conference on Interactions between Representation Theory, Quantum Field Theory, Category Theory, Mathematical Physics, and Quantum Information Theory, held in September 2007 at the University of Texas at Tyler. The papers in this volume, written by top experts in the field, address physical aspects, mathematical aspects, and foundational issues of quantum computation. This volume will benefit researchers interested in advances in quantum computation and communication, as well as graduate students who wish to enter the field of quantum computation.
Arithmetic And Algebraic Geometry
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Author : Yuri Tschinkel
language : en
Publisher: Springer Nature
Release Date : 2025-01-02
Arithmetic And Algebraic Geometry written by Yuri Tschinkel and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-02 with Mathematics categories.
This book is a tribute to the memory of Yuri Ivanovich Manin, who passed away on January 7, 2023. Manin was one of the giants of modern mathematics. His work covered a wide range of fields, including logic, number theory, geometry, mathematical physics, theoretical computer science, and linguistics. The contributions collected here are on topics close to his life-long passion: arithmetic and algebraic geometry.