Classical Lie Algebras at Infinity

Classical Lie Algebras at Infinity PDF Author: Ivan Penkov
Publisher: Springer Nature
ISBN: 3030896609
Category : Mathematics
Languages : en
Pages : 245

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Book Description
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.

Classical Lie Algebras at Infinity

Classical Lie Algebras at Infinity PDF Author: Ivan Penkov
Publisher: Springer Nature
ISBN: 3030896609
Category : Mathematics
Languages : en
Pages : 245

Get Book Here

Book Description
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

Stability in Modules for Classical Lie Algebras: A Constructive Approach PDF Author: Georgia Benkart
Publisher: American Mathematical Soc.
ISBN: 0821824929
Category : Mathematics
Languages : en
Pages : 177

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Book Description
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

Advances in Lie Superalgebras PDF Author: Maria Gorelik
Publisher: Springer Science & Business
ISBN: 3319029525
Category : Mathematics
Languages : en
Pages : 281

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Book Description
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.

Connected at infinity II: a selection of mathematics by Indians

Connected at infinity II: a selection of mathematics by Indians PDF Author: Rajendra Bhatia
Publisher: Springer
ISBN: 9386279568
Category : Mathematics
Languages : en
Pages : 193

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Book Description


Classical and Quantum Mechanics with Lie Algebras

Classical and Quantum Mechanics with Lie Algebras PDF Author: Yair Shapira
Publisher:
ISBN: 9789811240065
Category : Mechanics
Languages : en
Pages : 678

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Book Description


Perspectives in Lie Theory

Perspectives in Lie Theory PDF Author: Filippo Callegaro
Publisher: Springer
ISBN: 3319589717
Category : Mathematics
Languages : en
Pages : 465

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Book Description
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.

Infinite Dimensional Lie Algebras

Infinite Dimensional Lie Algebras PDF Author: Victor G. Kac
Publisher: Springer Science & Business Media
ISBN: 1475713827
Category : Mathematics
Languages : en
Pages : 267

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Book Description


An Introduction to Lie Groups and Lie Algebras

An Introduction to Lie Groups and Lie Algebras PDF Author: Alexander A. Kirillov
Publisher: Cambridge University Press
ISBN: 0521889693
Category : Mathematics
Languages : en
Pages : 237

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Book Description
This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.

Advances in Quantum Computation

Advances in Quantum Computation PDF Author: Kazem Mahdavi
Publisher: American Mathematical Soc.
ISBN: 0821846272
Category : Mathematics
Languages : en
Pages : 251

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Book Description
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.

Representation Theory

Representation Theory PDF Author: William Fulton
Publisher: Springer Science & Business Media
ISBN: 9780387974958
Category : Mathematics
Languages : en
Pages : 616

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Book Description
Introducing finite-dimensional representations of Lie groups and Lie algebras, this example-oriented book works from representation theory of finite groups, through Lie groups and Lie algrbras to the finite dimensional representations of the classical groups.