On Some Lie Bialgebra Structures on Polynomial Algebras and their Quantization

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. 625-662. ISSN 0010-3616

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Official URL: http://doi.org/10.1007/s00220-008-0554-x

Abstract

We study classical twists of Lie bialgebra structures on the polynomial current algebra g[u], where g is a simple complex finite-dimensional Lie algebra. We focus on the structures induced by the so-called quasi-trigonometric solutions of the classical Yang-Baxter equation. It turns out that quasi-trigonometric r-matrices fall into classes labelled by the vertices of the extended Dynkin diagram of g. We give complete classification of quasi-trigonometric r-matrices 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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