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On the structure of a real crossed group algebra

Published online by Cambridge University Press:  17 April 2009

P.P. Pálfy
P.P. Pálfy
Affiliation:
Mathematical Institute of the, Hungarian Academy of Sciences, Budapest, Pf. 127, H-1364, Hungary
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Abstract

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We prove that the crossed group algebra A of the infinite dihedral group over the real field defined by the generators a and b, relations b−1 ab = a−1, b2 = −1, and λa = aλ, λb = bλ for all real λ is a principal left ideal ring. This corrects a result of Buzási and provides the missing step towards the classification of finitely generated torsion-free RG-modules for groups G which contain an infinite cyclic subgroup of finite index.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 1 , February 1990 , pp. 113 - 115
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Buzási, K., ‘On the structure of a real crossed group algebra’, Bull. Austral. Math. Soc. 38 (1988), 31–40.CrossRefGoogle Scholar