Infinite Hopf Families of Algebras and Yang-Baxter Relations
نویسنده
چکیده
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 × 4 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.
منابع مشابه
Local Quasitriangular Hopf Algebras
We find a new class of Hopf algebras, local quasitriangular Hopf algebras, which generalize quasitriangular Hopf algebras. Using these Hopf algebras, we obtain solutions of the Yang-Baxter equation in a systematic way. That is, the category of modules with finite cycles over a local quasitriangular Hopf algebra is a braided tensor category.
متن کاملANALOGS OF q-SERRE RELATIONS IN THE YANG-BAXTER ALGEBRAS
1. Yang-Baxter algebras (YBA), introduced in [1, 2, 3], generalize the wideknown FRT construction [4] in the following sense: to any numerical matrix solution R of the Yang-Baxter equation there is associated a bialgebra containing the FRT one as a sub-bialgebra. Generally, this construction may provide examples of (new) bialgebras and Hopf algebras [5]. In several aspects, there is some simila...
متن کاملBulletin (new Series) of the American Mathematical Society
In his fundamental 1985 paper [6], Drinfeld attached a certain Hopf algebra, which he called a Yangian, to each finite dimensional simple Lie algebra over the ground field C. These Hopf algebras can be regarded as a tool for producing rational solutions of the quantum Yang-Baxter equation and are one of the main families of examples in Drinfeld's seminal ICM address [8] which marked the beginni...
متن کاملar X iv : q - a lg / 9 70 50 22 v 1 2 7 M ay 1 99 7 Coloured Hopf
Some new algebraic structures related to the coloured Yang-Baxter equation, and termed coloured Hopf algebras, are reviewed. Coloured quantum universal enveloping algebras of Lie algebras are defined in this context. An extension to the coloured graded Yang-Baxter equation and coloured Hopf superalgebras is also presented. The coloured two-parameter quantum universal enveloping algebra of gl(1/...
متن کاملInfinitesimal Hopf algebras
Infinitesimal bialgebras were introduced by Joni and Rota [J-R]. An infinitesimal bialgebra is at the same time an algebra and a coalgebra, in such a way that the comultiplication is a derivation. In this paper we define infinitesimal Hopf algebras, develop their basic theory and present several examples. It turns out that many properties of ordinary Hopf algebras possess an infinitesimal versi...
متن کامل