Invariant Drinfeld twists on group algebras
109 pages
English

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Invariant Drinfeld twists on group algebras

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109 pages
English
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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


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Nombre de lectures 14
Langue English

Exrait

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 algebrasOk(G)offunctions on finite non-abelian groups
We reformulate the problem in terms ofinvariant Drinfeld twists and obtain amethod to computeH2`(H)whenH=Ok(G)
IThe 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
II 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 algebrasOk(G)offunctions on finite non-abelian groups
We reformulate the problem in terms ofinvariant Drinfeld twists and obtain amethod to computeH2`(H)whenH=Ok(G)
IThe 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
II 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 algebrasOk(G)offunctions on finite non-abelian groups
We reformulate the problem in terms ofinvariant Drinfeld twists and obtain amethod to computeH`2(H)whenH=Ok(G)
IThe 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
II 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 algebrasOk(G)offunctions on finite non-abelian groups
We reformulate the problem in terms ofinvariant Drinfeld twists and obtain amethod to computeH`2(H)whenH=Ok(G)
IThe 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
II 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 algebrasOk(G)offunctions on finite non-abelian groups
We reformulate the problem in terms ofinvariant Drinfeld twists and obtain amethod to computeH`2(H)whenH=Ok(G)
IThe 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
II 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 algebrasOk(G)offunctions on finite non-abelian groups
We reformulate the problem in terms ofinvariant Drinfeld twists and obtain amethod to computeH2`(H)whenH=Ok(G)
IThe 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
II 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 H2`(H)of Hopf algebras that areneither cocommutative, nor pointedsuch as the Hopf algebrasOk(G)offunctions on finite non-abelian groups
We reformulate the problem in terms ofinvariant Drinfeld twists and obtain amethod to computeH2`(H)whenH=Ok(G)
IThe 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 H2`(H)of Hopf algebras that areneither cocommutative, nor pointedsuch as the Hopf algebrasOk(G)offunctions on finite non-abelian groups
We reformulate the problem in terms ofinvariant Drinfeld twists and obtain amethod to computeH2`(H)whenH=Ok(G)
IThe 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 algebrasOk(G)offunctions on finite non-abelian groups
We reformulate the problem in terms ofinvariant Drinfeld twists and obtain amethod to computeH2`(H)whenH=Ok(G)
IThe 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
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