Hyperbolicity of semigroup algebras

Let A be a finite-dimensional Q -algebra and Γ ⊂ A a Z -order. We classify those A with the property that Z 2 ▪ U ( Γ ) and refer to this as the hyperbolic property. We apply this in case A = K S is a semigroup algebra, with K = Q or K = Q ( − d ) . A complete classification is given when KS is semi...

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Bibliographic Details
Published in:Journal of algebra 2008-06, Vol.319 (12), p.5000-5015
Main Authors: Iwaki, E., Juriaans, S.O., Souza Filho, A.C.
Format: Article
Language:English
Subjects:
Group rings
Hyperbolic groups
Semigroup
Semigroup algebras
Units
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Summary:Let A be a finite-dimensional Q -algebra and Γ ⊂ A a Z -order. We classify those A with the property that Z 2 ▪ U ( Γ ) and refer to this as the hyperbolic property. We apply this in case A = K S is a semigroup algebra, with K = Q or K = Q ( − d ) . A complete classification is given when KS is semi-simple and also when S is a non-semi-simple semigroup.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2008.03.015