LEADER 00000nam a2200493 i 4500 
001    978-3-319-22704-7 
003    DE-He213 
005    20160512110847.0 
006    m     o  d         
007    cr nn 008maaau 
008    151224s2015    gw      s         0 eng d 
020    9783319227047|q(electronic bk.) 
020    9783319227030|q(paper) 
024 7  10.1007/978-3-319-22704-7|2doi 
040    GP|cGP|erda|dAS 
041 0  eng 
050  4 QA252.3|b.K43 2015 
082 04 512.482|223 
100 1  Kharchenko, Vladislav,|eauthor 
245 10 Quantum lie theory :|ba multilinear approach /|cby 
       Vladislav Kharchenko 
264  1 Cham :|bSpringer International Publishing :|bImprint: 
       Springer,|c2015 
300    1 online resource (xiii, 302 pages) :|billustrations, 
       digital ;|c24 cm 
336    text|btxt|2rdacontent 
337    computer|bc|2rdamedia 
338    online resource|bcr|2rdacarrier 
347    text file|bPDF|2rda 
490 1  Lecture notes in mathematics,|x0075-8434 ;|v2150 
505 0  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 
520    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 
650  0 Lie algebras 
650  0 Quantum theory 
650 14 Mathematics 
650 24 Associative Rings and Algebras 
650 24 Non-associative Rings and Algebras 
650 24 Group Theory and Generalizations 
650 24 Quantum Physics 
710 2  SpringerLink (Online service) 
773 0  |tSpringer eBooks 
830  0 Lecture notes in mathematics ;|v2150 
856 40 |uhttp://dx.doi.org/10.1007/978-3-319-22704-7
       |zeBook(Springerlink)