1.

Record Nr.

UNINA9910134869303321

Autore

Kharchenko Vladislav

Titolo

Quantum Lie Theory : A Multilinear Approach / / by Vladislav Kharchenko

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015

ISBN

3-319-22704-1

Edizione

[1st ed. 2015.]

Descrizione fisica

1 online resource (XIII, 302 p.)

Collana

Lecture Notes in Mathematics, , 0075-8434 ; ; 2150

Disciplina

512.55

Soggetti

Associative rings

Rings (Algebra)

Nonassociative rings

Group theory

Quantum theory

Associative Rings and Algebras

Non-associative Rings and Algebras

Group Theory and Generalizations

Quantum Physics

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

Elements of noncommutative algebra -- Poincar´e-Birkhoff-Witt basis -- Quantizations of Kac-Moody algebras -- Algebra of skew-primitive elements -- Multilinear operations -- Braided Hopf algebras -- Binary structures -- Algebra of primitive nonassociative polynomials.

Sommario/riassunto

This is an introduction to the mathematics behind the phrase “quantum Lie algebra”. The numerous attempts over the last 15-20 years to define a quantum Lie algebra as an elegant algebraic object with a binary “quantum” Lie bracket have not been widely accepted. In this book, an alternative approach is developed that includes multivariable operations. Among the problems discussed are the following: a PBW-type theorem; quantum deformations of Kac--Moody algebras; generic and symmetric quantum Lie operations; the Nichols algebras; the Gurevich--Manin  Lie algebras;  and Shestakov--Umirbaev  operations for the Lie theory of nonassociative products.  Opening with an



introduction for beginners and continuing as a textbook for graduate students in physics and mathematics, the book can also be used as a reference by more advanced readers. With the exception of the introductory chapter, the content of this monograph has not previously appeared in book form.