Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/existence-of-solutions-of-the-classical-yang-baxter-equation-for-a-QTC9PdXwX3
References (8)
-
Vyjayanthi Chari, A. Pressley (1994)
A guide to quantum groups -
N. Andruskiewitsch (2004)
On the automorphisms of Uq+(ℊ) -
W. Michaelis (1994)
A Class of Infinite-Dimensional Lie Bialgebras Containing the Virasoro AlgebraAdvances in Mathematics, 107
-
A. A. Belavin, V. G. Drinfel’D (1982)
Solutions of the classical Yang-Baxter equation for simple Lie algebrasFund. Anal. Appl., 16
-
V. Smedt (1994)
Existence of a Lie bialgebra structure on every Lie algebraLetters in Mathematical Physics, 31
-
J. Feldvoss (1999)
Existence of triangular Lie bialgebra structures IIJournal of Pure and Applied Algebra, 198
-
A. Belavin, V. Drinfel'd (1982)
Solutions of the classical Yang - Baxter equation for simple Lie algebrasFunctional Analysis and Its Applications, 16
-
W. Michaelis (1980)
Lie coalgebrasAdv. Math., 38
- Publisher
- Springer Journals
- Copyright
- Copyright © 2001 by Mathematische Seminar
- Subject
- Mathematics; Algebra; Differential Geometry; Combinatorics; Number Theory; Topology; Geometry
- ISSN
- 0025-5858
- eISSN
- 1865-8784
- DOI
- 10.1007/BF02941479
- Publisher site
- See Article on Publisher Site
Abstract
We characterize finite-dimensional Lie algebras over the real numbers for which the classical Yang-Baxter equation has a non-trivial skew-symmetric solution (resp. a non-trivial solution with invariant symmetric part). Equivalently, we obtain a characterization of those finite-dimensional real Lie algebras which admit a non-trivial (quasi-) triangular Lie bialgebra structure.
Journal
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg – Springer Journals
Published: Aug 28, 2008