Quantum lie theory, a multilinear approach
Kharchenko, Vladislav
Quantum lie theory : a multilinear approach [Documento electrónico] / Vladislav Kharchenko. - Cham : Springer International Publishing , 2015 . - XIII, 302 p.. - (Lecture notes in mathematics) 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.
Clicar aqui para aceder a um recurso externo
ISBN 978-3-319-22704-7
Álgebra
Teoria dos grupos
Teoria quântica
LCC QA251
Quantum lie theory : a multilinear approach [Documento electrónico] / Vladislav Kharchenko. - Cham : Springer International Publishing , 2015 . - XIII, 302 p.. - (Lecture notes in mathematics) 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.
Clicar aqui para aceder a um recurso externo
ISBN 978-3-319-22704-7
Álgebra
Teoria dos grupos
Teoria quântica
LCC QA251
