Hostname: page-component-77c89778f8-n9wrp Total loading time: 0 Render date: 2024-07-20T07:33:10.050Z Has data issue: false hasContentIssue false
  • English
  • Français

Factor Ideals of Some Representation Algebras

Published online by Cambridge University Press:  09 April 2009

W. D. Wallis
W. D. Wallis
Affiliation:
La Trobe UniversityMelbourne
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Throughout this paper F is an algebraically closed field of characteristic p (≠ 0) and g is a finite group whose order is divisible by p. We define in the usual way an F-representation of g (or F G-representation) and its corresponding module. The isomorphism class of the, F G-representation module M is written {M} or, where no confusion arises, M. A (G) denotes the F-representation algebra of G over the complex field G (as defined on pages 73 and 82 of [6]).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 9 , Issue 1-2 , February 1969 , pp. 109 - 123
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Bašev, V. A., ‘Representations of the group Z 2XZ 2 into a field of characteristic 2’, (Russian) Dokl. Akad. Nauk SSSR 141 (1961), 1015–1018.Google Scholar
[2]Conlon, S. B., ‘Twisted group algebras and their representations’, J. Aust. Math. Soc. 4 (1964), 152–173.CrossRefGoogle Scholar
[3]Conlon, S. B., ‘Certain representation algebras’, J. Aust. Math. Soc. 5 (1965), 83–99.CrossRefGoogle Scholar
[4]Conlon, S. B., ‘The modular representation algebra of groups with Sylow 2-subgroup Z2X2’, J. Aust. Math. Soc. 6 (1966), 76–88.CrossRefGoogle Scholar
[5]Conlon, S. B., ‘Structure in representation albegras’, J. of Algebra 5 (1967), 274–279.CrossRefGoogle Scholar
[6]Green, J. A., ‘A transfer theorem for modular representations’, J. of Algebra 1 (1964), 73–84.CrossRefGoogle Scholar
[7]Heller, A. and Reiner, I., ‘Indecomposable representations’, Illinois J. Math. 5 (1961), 314–323.CrossRefGoogle Scholar
[8]O'Reilly, M. F., ‘On the semisimplicity of the modular representation algebra of a finite group’, Illinois J. Math. 9 (1965), 261–276.Google Scholar
[9]Wielandt, H., Finite permutation groups (Academic Press, 1964).Google Scholar