vbid/9783319227047

Description

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.Typham this is the title: Quantum Lie Theory A Multilinear Approach