Semi-direct products of Hopf algebras

Semi-direct Products of Lie Algebras, Their Invariants and Representations

Introduction 1 1. Preliminaries 6 2. Generic stabilisers (centralisers) for the adjoint representation 9 3. Generic stabilisers for the coadjoint representation 10 4. Semi-direct products of Lie algebras and modules of covariants 12 5. Generic stabilisers and rational invariants for semi-direct products 14 6. Reductive semi-direct products and their polynomial invariants 21 7. Takiff Lie algebr...

Principal Ideals and Semi-direct Products in Commutative Banach Algebras

We prove necessary conditions for a commutative Banach algebra to be the semidirect product of some subalgebra together with a speci ed principal ideal. x

Full Crossed Products by Hopf C∗-algebras

We show that when a co-involutive Hopf C *-algebra S coacts via δ on a C *-algebra A, there exists a full crossed product A × δ S, with universal properties analogous to those of full crossed products by locally compact groups. The dual Hopf C *-algebra is then defined byˆS := C × id S.

Fibered Products of Hopf Algebras and Seifert-van Kampen Theorem for Semi-graphs of Tannakian Categories

It is known that Seifert-van Kampen theorem (for “good” topological spaces) can be showed by arguing the category of covering spaces. Similar arguments should be valid for abstract Galois categories (which Mochizuki calls ”connected anabelioids”) and neutral Tannakian categories. But when we try to state the theorem, the problem is the existence of amalgams (in other words, fibered coproducts) ...

On the Coderivations of Some Hopf Algebras