Infinite Hopf Families of Algebras and Yang-Baxter Relations

Details Infinite Hopf Families of Algebras and Yang-Baxter Relations Infinite Hopf Families of Algebras and Yang-Baxter Relations

2001-01-16

arxiv.org/abs/math-ph/0101018v1

Physics

Mathematical Physics

LaTeX, 16 pages

Scientific paper

A Yang-Baxter relation-based formalism for generalized quantum affine algebras with the structure of an infinite Hopf family of (super-) algebras is proposed. The structure of the infinite Hopf family is given explicitly on the level of $L$ matrices. The relation with the Drinfeld current realization is established in the case of $4\times4$ $R$-matrices by studying the analogue of the Ding-Frenkel theorem. By use of the concept of algebra ``comorphisms'' (which generalize the notion of algebra comodules for standard Hopf algebras), a possible way of constructing infinitely many commuting operators out of the generalized $RLL$ algebras is given. Finally some examples of the generalized $RLL$ algebras are briefly discussed.

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