Hyperbolicity of Semigroup Algebras

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

Hyperbolicity of Semigroup Algebras

Authors

Iwaki, E.

Juriaans, S. O.

Filho, A. C. Souza

Description

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 $n \in \{5,8,12\}$.
This article corresponds to the second chapter of the third author PhD Thesis