FRT-duals as quantum enveloping algebras

Coloured quantum universal enveloping algebras

We define some new algebraic structures, termed coloured Hopf algebras, by combining the coalgebra structures and antipodes of a standard Hopf algebra set H, corresponding to some parameter set Q, with the transformations of an algebra isomorphism group G, herein called colour group. Such transformations are labelled by some colour parameters, taking values in a colour set C. We show that vario...

Duals of coloured quantum universal enveloping algebras and coloured universal T -matrices

We extend the notion of dually conjugate Hopf (super)algebras to the coloured Hopf (super)algebras Hc that we recently introduced. We show that if the standard Hopf (super)algebras Hq that are the building blocks of Hc have Hopf duals H∗ q , then the latter may be used to construct coloured Hopf duals Hc∗, endowed with coloured algebra and antipode maps, but with a standard coalgebraic structur...

L ± Operators and Quantum Enveloping Algebras ∗

The relations between L operators and the generators in the quantum enveloping algebras are studied. The L operators for UqAN and UqG2 algebras are explicitly expressed by the generators as examples. ∗This work was supported by the National Natural Science Foundation of China and Grant No.LWTZ-1298 of Chinese Academy of Sciences. 1

Solutions to the quantum Yang–Baxter equation having certain Hopf algebras as their reduced FRT construction

Suppose that M is a finite-dimensional vector space over a field k and that R : M ⊗M −→M ⊗M is solution to the quantum Yang–Baxter equation(QYBE). The FRT construction [3] is a bialgebra A(R) associated with R in a natural way. There is a quotient of the FRT construction, referred to as the reduced FRT construction and denoted by Ã(R), which seems rather useful in computation [11]. The bialgebr...

Title: Q-schur Algebras as Quotients of Quantized Enveloping Algebras