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Hyperbolicity of Semigroup Algebras by Iwaki, E.; Juriaans, S. O.; Filho, A. C. Souza is a scholarly article available to read on EtoBox.

What is Hyperbolicity of Semigroup Algebras about?

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 $n \in \{5,8,12\}$.

Author

Iwaki, E.; Juriaans, S. O.; Filho, A. C. Souza

Published

2007

Language

EN