Triviality Theorems for Yetter-Drinfel'd Hopf Algebras
Rings and Algebras
2016-03-08 v2 Quantum Algebra
Representation Theory
Abstract
Under suitable assumptions on the base field, we prove that a commutative semisimple Yetter-Drinfel'd Hopf algebra over a finite abelian group is trivial, i.e., is an ordinary Hopf algebra, if its dimension is relatively prime to the order of the finite abelian group. Furthermore, we prove that a finite-dimensional cocommutative cosemisimple Yetter-Drinfel'd Hopf algebra contains a trivial Yetter-Drinfel'd Hopf subalgebra of dimension greater than one, at least if the Yetter-Drinfel'd Hopf algebra itself has dimension greater than one.
Keywords
Cite
@article{arxiv.1503.09181,
title = {Triviality Theorems for Yetter-Drinfel'd Hopf Algebras},
author = {Yorck Sommerhaeuser},
journal= {arXiv preprint arXiv:1503.09181},
year = {2016}
}
Comments
46 pages. Minute corrections in the second version. See also http://www.math.mun.ca/~sommerh/