Khoroshkin, S. M. and Pop, I. I. and Samsonov, M. E. and Stolin, A. A. and Tolstoy, V. N. (2007) On Some Lie Bialgebra Structures on Polynomial Algebras and their Quantization. Communications in Mathematical Physics, 282 (3). pp. 625662. ISSN 00103616

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Abstract
We study classical twists of Lie bialgebra structures on the polynomial current algebra g[u], where g is a simple complex finitedimensional Lie algebra. We focus on the structures induced by the socalled quasitrigonometric solutions of the classical YangBaxter equation. It turns out that quasitrigonometric rmatrices fall into classes labelled by the vertices of the extended Dynkin diagram of g. We give complete classification of quasitrigonometric rmatrices belonging to multiplicity free simple roots (which have coefficient 1 in the decomposition of the maximal root). We quantize solutions corresponding to the first root of sl(n).
Item Type:  Article 

Divisions:  School of Theoretical Physics > Preprints 
Date Deposited:  05 Oct 2017 19:23 
Last Modified:  16 Jul 2018 09:53 
URI:  http://dair.dias.ie/id/eprint/216 
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