Decompositions of quasigraded Lie algebras, non-skew-symmetric classical r-matrices and generalized Gaudin models

JOURNAL OF GEOMETRY AND PHYSICS

卷:75

Article

Skrypnyk, T.^1,2 

[1] Univ Milano Bicocca, I-20125 Milan, Italy

[2] Bogoliubov Inst Theoret Phys, UA-03143 Kiev, Ukraine

关键词: Infinite-dimensional Lie algebras;    Classical r-matrices;    Gaudin-type systems;   

DOI  :  10.1016/j.geomphys.2013.09.001

来源: Elsevier

【 摘 要 】

We construct a special family of quasigraded Lie algebras that generalize loop algebras in different gradings and admit Adler-Kostant-Symes decomposition into a sum of two subalgebras. We analyze the special cases when the constructed Lie algebras admit additionally other types of Adler-Kostant-Symes decompositions. Based on the proposed Lie algebras and their decompositions we explicitly construct several new classes of non-skew-symmetric classical r-matrices r(u, v) with spectral parameters. Using them we obtain new types of the generalized quantum and classical Gaudin spin chains. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free