Grothendieck Rings of 2$n^2$ dimensional Hopf Algebras $H_{2n^2}$
Abstract
In this paper, we construct the Grothendieck ring of a class of 2$n^2$-dimension semisimple Hopf Algebras $H_{2n^2}$, which can be viewed as a generalization of the 8-dimension Kac-Paljutkin Hopf algebra $K_8$. All irreducible $H_{2n^2}$-modules are classified. Furthermore, we describe the Grothendieck ring $r(H_{2n^2})$ by generators and relations explicitly.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2018
- DOI:
- 10.48550/arXiv.1809.00766
- arXiv:
- arXiv:1809.00766
- Bibcode:
- 2018arXiv180900766C
- Keywords:
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- Mathematics - Rings and Algebras;
- Mathematics - Representation Theory;
- 16G10;
- 16D70;
- 16T99
- E-Print:
- 18 pages