# 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…

## 2 Citations

### McKay matrix for indecomposable module of finite representation type Hopf algebra

- MathematicsCommunications 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…

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