Galois Objects over Generalized Drinfeld Doubles, with an Application to uq(sl2)
✍ Scribed by Peter Schauenburg
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 130 KB
- Volume
- 217
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
Ralf Gunther has determined all the cleft extensions over the finite quotient ¨Ž .
Hopf algebra u ᒐ ᒉ of the quantized universal enveloping algebra of ᒐ ᒉ at a q 2 2 w x root of unity R. Gunther, Ph.D. thesis, Universitat Munchen, 1999 . His tech-¨¨Ž . niques applications of the diamond lemma are similar to those used by A. w Ž . x Masuoka Comm. Algebra 22 1994 , 4537᎐4559 for the two-generator Taft algebras. In the present paper we give another proof of a special case of Gunther's Ž . classification, namely, the case of cleft Galois extensions of the base field. The Ž . idea is that u ᒐ ᒉ is the quotient of the Drinfeld double of a Taft algebra by a q 2
normal Hopf subalgebra. We use techniques that allow us to calculate all Galois objects of such a composed Hopf algebra.
ᮊ 1999 Academic Press B Ž . xy m y g A m H is a bijection. We denote by Gal H the set of all Ž0.
Ž 1. B isomorphism classes of right H-Galois extensions of B which are faithfully flat as left B-modules. In the case that B s k we say that A is an Ž .