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The classification of finite-dimensional pointed Hopf algebras over an algebraically closed field of characteristic zero and whose group of group-like elements is abelian is very much completed. However, from a more categorical point of view it would make sense to classify such Hopf algebras up to gauge equivalence,i.e. two (quasi-)Hopf algebras are called gauge equivalent if their representation categories are tensor equivalent.

Are people interested in the latter problem? Are there results in this direction?

Edit: In this paper by Wakui, he classified all $8$-dimensional Hopf-algebras up to gauge equivalence. In fact the representation ring alone distinguishes between these Hopf-algebras. Clearly people are interested in this. Are there further results?

The classification of finite-dimensional pointed Hopf algebras over an algebraically closed field of characteristic zero and whose group of group-like elements is abelian is very much completed. However, from a more categorical point of view it would make sense to classify such Hopf algebras up to gauge equivalence,i.e. two (quasi-)Hopf algebras are called gauge equivalent if their representation categories are tensor equivalent.

Are people interested in the latter problem? Are there results in this direction?

The classification of finite-dimensional pointed Hopf algebras over an algebraically closed field of characteristic zero and whose group of group-like elements is abelian is very much completed. However, from a more categorical point of view it would make sense to classify such Hopf algebras up to gauge equivalence,i.e. two (quasi-)Hopf algebras are called gauge equivalent if their representation categories are tensor equivalent.

Are people interested in the latter problem? Are there results in this direction?

Edit: In this paper by Wakui, he classified all $8$-dimensional Hopf-algebras up to gauge equivalence. In fact the representation ring alone distinguishes between these Hopf-algebras. Clearly people are interested in this. Are there further results?

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Mathematician 42
Mathematician 42
  • 395
  • 1
  • 11

The classification of finite-dimensional pointed Hopf algebras over an algebraically closed field of characteristic zero and whose group of group-like elements is abelian is very much completed. However, from a more categorical point of view it would make sense to classify such Hopf algebras up to gauge equivalence,i.e. two (quasi-)Hopf algebras are called gauge equivalent if their representationsrepresentation categories are tensor equivalent.

Are people interested in the latter problem? Are there results in this direction?

The classification of finite-dimensional pointed Hopf algebras over an algebraically closed field of characteristic zero and whose group of group-like elements is abelian is very much completed. However, from a more categorical point of view it would make sense to classify such Hopf algebras up to gauge equivalence,i.e. two (quasi-)Hopf algebras are called gauge equivalent if their representations categories are tensor equivalent.

Are people interested in the latter problem? Are there results in this direction?

The classification of finite-dimensional pointed Hopf algebras over an algebraically closed field of characteristic zero and whose group of group-like elements is abelian is very much completed. However, from a more categorical point of view it would make sense to classify such Hopf algebras up to gauge equivalence,i.e. two (quasi-)Hopf algebras are called gauge equivalent if their representation categories are tensor equivalent.

Are people interested in the latter problem? Are there results in this direction?

Source Link
Mathematician 42
Mathematician 42
  • 395
  • 1
  • 11

Classification of pointed Hopf algebras up to gauge equivalence

The classification of finite-dimensional pointed Hopf algebras over an algebraically closed field of characteristic zero and whose group of group-like elements is abelian is very much completed. However, from a more categorical point of view it would make sense to classify such Hopf algebras up to gauge equivalence,i.e. two (quasi-)Hopf algebras are called gauge equivalent if their representations categories are tensor equivalent.

Are people interested in the latter problem? Are there results in this direction?