Generalized Gaudin spin chains, nonskew symmetric r-matrices, and reflection equation algebras

Journal Article · Thu Nov 15 00:00:00 EST 2007 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2816256· OSTI ID:21013793

Skrypnyk, T ^[1]

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1. Bogoliubov Institute for Theoretical Physics of NASU, Metrologichna st.14-b, Kiev 03143 (Ukraine)

Using a one-parametric family of automorphisms {sigma}(u) of finite-dimensional simple Lie algebras g and classical skew-symmetric r-matrices r{sub 12}(u-v), we construct ''twisted'' nonskew symmetric classical r-matrices r{sub 12}{sup {sigma}}(u,v) with spectral parameters. We show that in the special case {sigma}(u)=Ad{sub K(u)} and classical matrix Lie algebras g, they are connected with the quasiclassical limit of the reflection equation algebras. Using them and results of our previous papers, we construct new integrable quantum spin chains of the ''generalized Gaudin'' type with an arbitrary value of spin living at each site.

• OSTI ID: 21013793
• Journal Information: Journal of Mathematical Physics, Vol. 48, Issue 11; Other Information: DOI: 10.1063/1.2816256; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
EQUATIONS
INTEGRAL CALCULUS
LIE GROUPS
QUANTUM MECHANICS
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SPIN