The Grothendieck Group of Hopf Algebras

Details The Grothendieck Group of Hopf Algebras The Grothendieck Group of Hopf Algebras

2003-10-24

arxiv.org/abs/math/0310388v3

Journal of Pure and Applied Algebra 194 (2004) 85 - 93

Mathematics

Rings and Algebras

9 pages, accepted to Journal of Pure and Applied Algebra entitled "Representations of degree three for semisimple Hopf algebra

Scientific paper

Let H be a cosemisimple Hopf algebra over an algebraically closed field k which contains a simple subcoalgebra of dimension 9. We show that if H has no simple subcoalgebras of even dimension then H contains either a grouplike element with order 2 or 3, a Hopf subalgebra of dimension 75, or a family of simple subcoalgebras whose dimensions are the squares of each positive odd integer. In particular, if H is finite odd dimensional, then its dimension is divisible by 3.

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