Quantum Lie Theory: A Multilinear Approach (lecture Notes In Mathematics)
by Vladislav Kharchenko /
2016 / English / PDF
3 MB Download
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.
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.
