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arXiv · 0704.2248

Hyperbolicity of Semigroup Algebras

E. Iwaki·S. O. Juriaans·A. C. Souza Filho
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Abstract

Let $A$ be a finite dimensional $Q-$algebra and $Γsubset A$ a $Z-$order. We classify those $A$ with the property that $Z^2$ does not embed in $\mathcal{U}(Γ)$. 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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BibTeXRIS

E. Iwaki, S. O. Juriaans, A. C. Souza Filho. 2007-11-21. Hyperbolicity of Semigroup Algebras. https://arxiv.org/abs/0704.2248

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