McKay matrices for finite-dimensional Hopf algebras

@article{Benkart2020McKayMF,
  title={McKay matrices for finite-dimensional Hopf algebras},
  author={Georgia Benkart and Rekha Biswal and Ellen E. Kirkman and Van C. Nguyen and Jieru Zhu},
  journal={Canadian Journal of Mathematics},
  year={2020},
  volume={74},
  pages={686 - 731}
}
Abstract For a finite-dimensional Hopf algebra $\mathsf {A}$ , the McKay matrix $\mathsf {M}_{\mathsf {V}}$ of an $\mathsf {A}$ -module $\mathsf {V}$ encodes the relations for tensoring the simple $\mathsf {A}$ -modules with $\mathsf {V}$ . We prove results about the eigenvalues and the right and left (generalized) eigenvectors of $\mathsf {M}_{\mathsf {V}}$ by relating them to characters. We show how the projective McKay matrix $\mathsf {Q}_{\mathsf {V}}$ obtained by tensoring… 

McKay matrix for indecomposable module of finite representation type Hopf algebra

Abstract Let H be a Hopf algebra of finite representation type. For the grouplike elements and skew-primitive elements in H, we prove some general results about the eigenvalues and eigenvectors of

References

SHOWING 1-10 OF 49 REFERENCES

The monoidal center and the character algebra

Higman Ideals and Verlinde-type Formulas for Hopf Algebras

We offer a comprehensive discussion on Verlinde-type formulas for Hopf algebras H over an algebraically closed field of characteristic 0. Some of the results are new and some are known, but are

Representations of Finite-Dimensional Hopf Algebras

Abstract LetHdenote a finite-dimensional Hopf algebra with antipodeSover a field k . We give a new proof of the fact, due to OS , thatHis a symmetric algebra if and only ifHis unimodular andS2is

Characters and a Verlinde-type formula for symmetric Hopf algebras

REPRESENTATIONS OF A CLASS OF DRINFELD'S DOUBLES

Let k be a field and An(ω) be the Taft's n2-dimensional Hopf algebra. When n is odd, the Drinfeld quantum double D(An(ω)) of An(ω) is a ribbon Hopf algebra. In the previous articles, we constructed

Finite-Dimensional Representations of a Quantum Double

Abstract Let k be a field and let A n (ω) be the Taft's n 2 -dimensional Hopf algebra. When n is odd, the Drinfeld quantum double D ( A n (ω)) of A n (ω) is a ribbon Hopf algebra. In a previous paper

Structure constants related to symmetric Hopf algebras

Conjugacy Classes, Class Sums and Character Tables for Hopf Algebras

We extend the notion of conjugacy classes and class sums from finite groups to semisimple Hopf algebras and show that the conjugacy classes are obtained from the factorization of H as irreducible