Hyperbolicity of Semigroup Algebras

Details Hyperbolicity of Semigroup Algebras Hyperbolicity of Semigroup Algebras

2007-04-17

arxiv.org/abs/0704.2248v2

Mathematics

Rings and Algebras

This article corresponds to the second chapter of the third author PhD Thesis

Scientific paper

Let $A$ be a finite dimensional $Q-$algebra and $\Gamma subset A$ a $Z-$order. We classify those $A$ with the property that $Z^2$ does not embed in $\mathcal{U}(\Gamma)$. We call this last property the hyperbolic property. We apply this in the case that $A = KS$ a semigroup algebra with $K = Q$ or $K = Q(\sqrt{-d})$. In particular, when $KS$ is semi-simple and has no nilpotent elements, we prove that $S$ is an inverse semigroup which is the disjoint union of Higman groups and at most one cyclic group $C_n$ with $n \in \{5,8,12\}$.

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