# 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 Kirkman and Van C. Nguyen and Jieru Zhu},
year={2020},
volume={74},
pages={686 - 731}
}
• Published 10 July 2020
• Mathematics
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…
2 Citations
• Mathematics
Communications in Algebra
• 2022
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

• Mathematics
• 2010
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
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
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
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
• Mathematics
• 2011
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