Invariant Drinfeld twists on group algebras

Christian Kassel

Description

Invariant Drinfeld twists on group algebras Christian Kassel Institut de Recherche Mathematique Avancee CNRS - Universite de Strasbourg Strasbourg, France International Workshop “Groups and Hopf Algebras” Memorial University of Newfoundland 5 June 2009

• quantum group


• group h2


• drinfeld twists


• hopf algebras


• class-preserving outer


• invariant drinfeld


• group algebras

Sujets

• Kassel
• Memorial University of Newfoundland
• Guillot
• Quantum group

Informations

• Publié par: pefav
• Nombre de lectures: 14
• Langue: English

Extrait

Invariant Drinfeld twists on group algebras

Christian Kassel

InstitutdeRechercheMath ´ ematiqueAvance ´ e CNRS - Universit  ´e  de Strasbourg Strasbourg, France

International Workshop “Groups and Hopf Algebras” Memorial University of Newfoundland 5 June 2009

Introduction

I

I

I

Report on joint work withPierre Guillot(Strasbourg): Cohomology of invariant Drinfeld twists on group algebras arXiv:0903.2807

Our original motivation was to compute the secondlazy cohomology group H ` 2 (H)of Hopf algebras that areneither cocommutative, nor pointedsuch as the Hopf algebrasO k (G)offunctions on finite non-abelian groups

We reformulate the problem in terms ofinvariant Drinfeld twists and obtain amethod to computeH 2 ` (H)whenH=O k (G)

I The answer involves theabelian normal subgroups of central typeofG as well as the group ofclass-preserving outer automorphismsofG

The proof uses tools fromquantum group theory, mainlyR-matrices

I I shall illustrate all this with severalexamples

Introduction

I

I

I

Report on joint work withPierre Guillot(Strasbourg): Cohomology of invariant Drinfeld twists on group algebras arXiv:0903.2807

Our original motivation was to compute the secondlazy cohomology group H ` 2 (H)of Hopf algebras that areneither cocommutative, nor pointedsuch as the Hopf algebrasO k (G)offunctions on finite non-abelian groups

We reformulate the problem in terms ofinvariant Drinfeld twists and obtain amethod to computeH 2 ` (H)whenH=O k (G)

I The answer involves theabelian normal subgroups of central typeofG as well as the group ofclass-preserving outer automorphismsofG

The proof uses tools fromquantum group theory, mainlyR-matrices

I I shall illustrate all this with severalexamples

Introduction

I

I

I

Report on joint work withPierre Guillot(Strasbourg): Cohomology of invariant Drinfeld twists on group algebras arXiv:0903.2807

Our original motivation was to compute the secondlazy cohomology group H ` 2 (H)of Hopf algebras that areneither cocommutative, nor pointedsuch as the Hopf algebrasO k (G)offunctions on finite non-abelian groups

We reformulate the problem in terms ofinvariant Drinfeld twists and obtain amethod to computeH ` 2 (H)whenH=O k (G)

I The answer involves theabelian normal subgroups of central typeofG as well as the group ofclass-preserving outer automorphismsofG

The proof uses tools fromquantum group theory, mainlyR-matrices

I I shall illustrate all this with severalexamples

Introduction

I

I

I

Report on joint work withPierre Guillot(Strasbourg): Cohomology of invariant Drinfeld twists on group algebras arXiv:0903.2807

Our original motivation was to compute the secondlazy cohomology group H ` 2 (H)of Hopf algebras that areneither cocommutative, nor pointedsuch as the Hopf algebrasO k (G)offunctions on finite non-abelian groups

We reformulate the problem in terms ofinvariant Drinfeld twists and obtain amethod to computeH ` 2 (H)whenH=O k (G)

I The answer involves theabelian normal subgroups of central typeofG as well as the group ofclass-preserving outer automorphismsofG

The proof uses tools fromquantum group theory, mainlyR-matrices

I I shall illustrate all this with severalexamples

Introduction

I

I

I

Report on joint work withPierre Guillot(Strasbourg): Cohomology of invariant Drinfeld twists on group algebras arXiv:0903.2807

Our original motivation was to compute the secondlazy cohomology group H ` 2 (H)of Hopf algebras that areneither cocommutative, nor pointedsuch as the Hopf algebrasO k (G)offunctions on finite non-abelian groups

We reformulate the problem in terms ofinvariant Drinfeld twists and obtain amethod to computeH ` 2 (H)whenH=O k (G)

I The answer involves theabelian normal subgroups of central typeofG as well as the group ofclass-preserving outer automorphismsofG

The proof uses tools fromquantum group theory, mainlyR-matrices

I I shall illustrate all this with severalexamples

Introduction

I

I

I

Report on joint work withPierre Guillot(Strasbourg): Cohomology of invariant Drinfeld twists on group algebras arXiv:0903.2807

Our original motivation was to compute the secondlazy cohomology group H ` 2 (H)of Hopf algebras that areneither cocommutative, nor pointedsuch as the Hopf algebrasO k (G)offunctions on finite non-abelian groups

We reformulate the problem in terms ofinvariant Drinfeld twists and obtain amethod to computeH 2 ` (H)whenH=O k (G)

I The answer involves theabelian normal subgroups of central typeofG as well as the group ofclass-preserving outer automorphismsofG

The proof uses tools fromquantum group theory, mainlyR-matrices

I I shall illustrate all this with severalexamples

Introduction

I

I

I

Report on joint work withPierre Guillot(Strasbourg): Cohomology of invariant Drinfeld twists on group algebras arXiv:0903.2807

Our original motivation was to compute the secondlazy cohomology group H 2 ` (H)of Hopf algebras that areneither cocommutative, nor pointedsuch as the Hopf algebrasO k (G)offunctions on finite non-abelian groups

We reformulate the problem in terms ofinvariant Drinfeld twists and obtain amethod to computeH 2 ` (H)whenH=O k (G)

I The answer involves theabelian normal subgroups of central typeofG as well as the group ofclass-preserving outer automorphismsofG

I

The proof uses tools fromquantum group theory, mainlyR-matrices

I shall illustrate all this with severalexamples

Introduction

I

I

I

Report on joint work withPierre Guillot(Strasbourg): Cohomology of invariant Drinfeld twists on group algebras arXiv:0903.2807

Our original motivation was to compute the secondlazy cohomology group H 2 ` (H)of Hopf algebras that areneither cocommutative, nor pointedsuch as the Hopf algebrasO k (G)offunctions on finite non-abelian groups

We reformulate the problem in terms ofinvariant Drinfeld twists and obtain amethod to computeH 2 ` (H)whenH=O k (G)

I The answer involves theabelian normal subgroups of central typeofG as well as the group ofclass-preserving outer automorphismsofG

I

The proof uses tools fromquantum group theory, mainlyR-matrices

I shall illustrate all this with severalexamples

Introduction

I

I

I

Report on joint work withPierre Guillot(Strasbourg): Cohomology of invariant Drinfeld twists on group algebras arXiv:0903.2807

Our original motivation was to compute the secondlazy cohomology group H ` 2 (H)of Hopf algebras that areneither cocommutative, nor pointedsuch as the Hopf algebrasO k (G)offunctions on finite non-abelian groups

We reformulate the problem in terms ofinvariant Drinfeld twists and obtain amethod to computeH 2 ` (H)whenH=O k (G)

I The answer involves theabelian normal subgroups of central typeofG as well as the group ofclass-preserving outer automorphismsofG

I

The proof uses tools fromquantum group theory, mainlyR-matrices

I shall illustrate all this with severalexamples