Some of the first examples of Hopf algebras described over a field k w x which are neither commutative nor cocommutative 13, 14 involve elements a and x which satisfy the relations β¬ a s a m a, β¬ x s x m a q 1 m x, and xa s qax Ε½ . Ε½ . for some q g k \_ 0. With the advent of quantum groups these re
Coideal Subalgebras in Finite Hopf Algebras
β Scribed by A. Masuoka
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 388 KB
- Volume
- 163
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let H denote a finite-dimensional Hopf algebra with antipode S over a field β«ήβ¬ -. w We give a new proof of the fact, due to Oberst and Schneider Manuscripta Math. 8 Ε½ . x 1973 , 217α241 , that H is a symmetric algebra if and only if H is unimodular and S 2 is inner. If H is involutory and not sem
Let Bΰ » H be a crossed product algebra over an algebraically closed field, with H a finite dimensional Hopf algebra. We give an explicit equivalence between the category of finite dimensional Bΰ » H-modules whose restriction to B is a direct sum of copies of a stable irreducible B-module, and the categ
Let G be a finite algebraic group, defined over an algebraically closed field k of characteristic p>0. Such a group decomposes into a semidirect product G=G 0 \_G red with a constant group G red and a normal infinitesimal subgroup G 0 . If the principal block B 0 (G) of the group algebra H(G) has fi
Some finiteness conditions for infinite dimensional coalgebras, particularly right or left semiperfect coalgebras, or co-Frobenius Hopf algebras are studied. As well, examples of co-Frobenius Hopf algebras are constructed via a Hopf algebra structure on an Ore extension of a group algebra, and it is