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On Biproducts and Extensions

Yevgenia Kashina, Yorck Sommerhaeuser

Abstract

We describe in which ways the Radford biproducts of certain eight-dimensional Yetter-Drinfel'd Hopf algebras over the elementary abelian group of order 4 can be written as extensions of Hopf algebras.

On Biproducts and Extensions

Abstract

We describe in which ways the Radford biproducts of certain eight-dimensional Yetter-Drinfel'd Hopf algebras over the elementary abelian group of order 4 can be written as extensions of Hopf algebras.

Paper Structure

This paper contains 7 sections, 31 theorems, 130 equations.

Table of Contents

  1. Preliminaries
  2. The biproduct in the first case
  3. Representations
  4. Hopf subalgebras of dimension $16$
  5. Hopf subalgebras of dimension $2$
  6. Hopf subalgebras of dimensions $4$ and $8$
  7. The biproduct in the second case

Key Result

Proposition 1

Suppose that $B$ is an algebra and that $f_A \colon A \rightarrow B$ as well as $f_H \colon H \rightarrow B$ are $K$-linear maps. Then the following assertions are equivalent:

Theorems & Definitions (62)

  • Definition
  • Proposition
  • Proof
  • Corollary
  • Definition
  • Definition
  • Proposition
  • Proof
  • Proposition
  • Proof
  • ...and 52 more