A nonlinear deformed su(2) algebra with a two-color quasitriangular Hopf structure
- Institute of Nuclear Physics, NCSR Demokritos, GR-15310 Aghia Paraskevi, Attiki (Greece)
- Department of Physics, Aristotle University of Thessaloniki, GR-54006 Thessaloniki (Greece)
- Department of Theoretical Physics, Faculty of Physics, University of Bucharest, Bucharest-Magurele, P.O. Box MG-5211 (Romania)
- Physique Nucleaire Theorique et Physique Mathematique, Universite Libre de Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, B-1050 Brussels (Belgium)
Nonlinear deformations of the enveloping algebra of su(2), involving two arbitrary functions of J{sub 0} and generalizing the Witten algebra, were introduced some time ago by Delbecq and Quesne. In the present paper, the problem of endowing some of them with a Hopf algebraic structure is addressed by studying in detail a specific example, referred to as scr(A){sub q}{sup +}(1). This algebra is shown to possess two series of (N+1)-dimensional unitary irreducible representations, where N=0,1,2,{hor_ellipsis}. To allow the coupling of any two such representations, a generalization of the standard Hopf axioms is proposed by proceeding in two steps. In the first one, a variant and extension of the deforming functional technique is introduced: variant because a map between two deformed algebras, su{sub q}(2) and scr(A){sub q}{sup +}(1), is considered instead of a map between a Lie algebra and a deformed one, and extension because use is made of a two-valued functional, whose inverse is singular. As a result, the Hopf structure of su{sub q}(2) is carried over to scr(A){sub q}{sup +}(1), thereby endowing the latter with a double Hopf structure. In the second step, the definition of the coproduct, counit, antipode, and scr(R)-matrix is extended so that the double Hopf algebra is enlarged into a new algebraic structure. The latter is referred to as a two-color quasitriangular Hopf algebra because the corresponding scr(R)-matrix is a solution of the colored Yang{endash}Baxter equation, where the {open_quotes}color{close_quotes} parameters take two discrete values associated with the two series of finite-dimensional representations. {copyright} {ital 1997 American Institute of Physics.}
- OSTI ID:
- 435152
- Journal Information:
- Journal of Mathematical Physics, Vol. 38, Issue 1; Other Information: PBD: Jan 1997
- Country of Publication:
- United States
- Language:
- English
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