Quantum Lie Theory
A Multilinear Approach
Seiten
2015
|
1st ed. 2015
Springer International Publishing (Verlag)
978-3-319-22703-0 (ISBN)
Springer International Publishing (Verlag)
978-3-319-22703-0 (ISBN)
lt;p>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.
lt;p>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.
Erscheint lt. Verlag | 25.12.2015 |
---|---|
Reihe/Serie | Lecture Notes in Mathematics |
Zusatzinfo | XIII, 302 p. |
Verlagsort | Cham |
Sprache | englisch |
Maße | 155 x 235 mm |
Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
Naturwissenschaften ► Physik / Astronomie ► Quantenphysik | |
Schlagworte | 17B37,20G42,16T20,16T05,17A50,17B75,17B81,17B81,81 • 17B37,20G42,16T20,16T05,17A50,17B75,17B81,17B81,81R50 • Associative rings and algebras • braided space • character Hopf algebra • Group Theory and Generalizations • mathematics and statistics • Nichols algebra • non-associative rings and algebras • Poincaré-Birkhoff-Witt basis, • Quantum Lie operation, • Quantum Physics |
ISBN-10 | 3-319-22703-3 / 3319227033 |
ISBN-13 | 978-3-319-22703-0 / 9783319227030 |
Zustand | Neuware |
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