2 Γ 2 . If H is abelian of order 8, we may use K = k H \* , and if H is abelian of order 4 we use K = kD 8 \* . If H βΌ = D 8 , then in the two possible examples, one has K = kD 8 \* and the other has K = kQ 8 \* . If H βΌ = 2 Γ 2 Γ 2 then H has two simple degree 2 characters, Ο 1 and Ο 2 , and they
Spectral Sequences for the Classification of Extensions of Hopf Algebras
β Scribed by Gregory D. Henderson
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 322 KB
- Volume
- 193
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
β¦ Synopsis
We construct spectral sequences which provide a way to compute the cohomology theory that classifies extensions of graded connected Hopf algebras over a Ε½ . commutative ring as described by William M. Singer. Specifically, for A, B an abelian matched pair of graded connected R-Hopf algebras, we construct a pair of
these spectral sequences, we examine the special case of B a monogenic graded connected Hopf algebra and also analyze an extension of Hopf algebras given by James P. Lin.
π SIMILAR VOLUMES
The main result in this paper states that every strongly graded bialgebra whose component of grade 1 is a finite-dimensional Hopf algebra is itself a Hopf algebra. This fact is used to obtain a group cohomology classification of strongly graded Hopf algebras, with 1-component of finite dimension, fr
## dedicated to helmut wielandt on his 90th birthday We show that the length l V of the spectral sequence of a Lie algebra extension acting on a module V with a submodule W is not bounded by any function of the lengths l V/W and l W .
Let p be an odd prime and n a positive integer and let k be a field of Ε½ . r p and let r denote the largest integer between 0 and n such that K l k s p Ε½ . r r r k , where denotes a primitive p th root of unity. The extension Krk is p p separable, but not necessarily normal and, by Greither and Pa