BLM realization for the integral form of quantum 𝔤𝔩n

Let U(n) be the quantum enveloping algebra of 𝔤𝔩n over ℚ(v). We will use q-Schur algebras to realize the Lusztig integral form of U(n). Furthermore, we will use this result to realize quantum 𝔤𝔩n over k, where k is a field containing an lth primitive root ε of 1 with l ≥ 1 odd.

DOUBLE LOOP QUANTUM ENVELOPING ALGEBRAS

In this paper we describe certain homological properties and representations of a two-parameter quantum enveloping algebra Ug, h of 𝔰𝔩(2), where g, h are group-like elements.

Compact Hopf *-Algebras, Quantum Enveloping Algebras and Dual Woronowicz Algebras for Quantum Lorentz Groups

A compact Hopf *-algebra is a compact quantum group in the sense of Koornwinder. There exists an injective functor from the category of compact Hopf *-algebras to the category of compact Woronowicz algebras. A definition of the quantum enveloping algebra Uq(sl(n,C)) is given. For quantum groups SUq(n) and SLq(n,C), the commutant of a canonical representation of the quantum enveloping algebra for q coincides with the commutant of the dual Woronowicz algebra for q-1.