TY  - BOOK
AU  - Kharchenko,Vladislav
ED  - SpringerLink (Online service)
TI  - Quantum Lie Theory: A Multilinear Approach 
T2  - Lecture Notes in Mathematics,
SN  - 9783319227047
AV  - QA251.5 
U1  - 512.46 23
PY  - 2015///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Associative rings
KW  - Rings (Algebra)
KW  - Nonassociative rings
KW  - Group theory
KW  - Quantum physics
KW  - Associative Rings and Algebras
KW  - Non-associative Rings and Algebras
KW  - Group Theory and Generalizations
KW  - Quantum Physics
N1  - 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
N2  - 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
UR  - https://doi.org/10.1007/978-3-319-22704-7
ER  -