Kharchenko, Vladislav.
Quantum Lie Theory A Multilinear Approach / [electronic resource] : by Vladislav Kharchenko. - 1st ed. 2015. - XIII, 302 p. online resource. - Lecture Notes in Mathematics, 2150 0075-8434 ; . - Lecture Notes in Mathematics, 2150 .
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.
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.
9783319227047
10.1007/978-3-319-22704-7 doi
Associative rings.
Rings (Algebra).
Nonassociative rings.
Group theory.
Quantum physics.
Associative Rings and Algebras.
Non-associative Rings and Algebras.
Group Theory and Generalizations.
Quantum Physics.
QA251.5
512.46
Quantum Lie Theory A Multilinear Approach / [electronic resource] : by Vladislav Kharchenko. - 1st ed. 2015. - XIII, 302 p. online resource. - Lecture Notes in Mathematics, 2150 0075-8434 ; . - Lecture Notes in Mathematics, 2150 .
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.
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.
9783319227047
10.1007/978-3-319-22704-7 doi
Associative rings.
Rings (Algebra).
Nonassociative rings.
Group theory.
Quantum physics.
Associative Rings and Algebras.
Non-associative Rings and Algebras.
Group Theory and Generalizations.
Quantum Physics.
QA251.5
512.46