Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-10T16:54:39.254Z Has data issue: false hasContentIssue false
  • English
  • Français

Roots of Simple Modules

Published online by Cambridge University Press:  20 November 2018

Burkhard Külshammer
Burkhard Külshammer*
Affiliation:
Mathematisches Institut, Friedrich-Schiller-Universität, 07737 Jena, Germany e-mail: kuelshammer@uni-jena.de
Rights & Permissions [Opens in a new window]

Abstract

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.

We introduce roots of indecomposable modules over group algebras of finite groups, and we investigate some of their properties. This allows us to correct an error in Landrock's book which has to do with roots of simple modules.

Keywords

20C2020C05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 49 , Issue 1 , 01 March 2006 , pp. 96 - 107
Copyright
Copyright © Canadian Mathematical Society 2006

References

[1] Alperin, J.,Weights for finite groups. Proc. Symp. Pure Math. 47(1987), 369–379.Google Scholar
[2] Alperin, J. and Broué, M., Local methods in block theory. Ann. Math. (2) 110(1979), 143–157.Google Scholar
[3] Barker, L., On p-soluble groups and the number of simple modules associated with a given Brauer pair. Quart. J. Math. Oxford Ser. (2) 48(1997), 133–160.Google Scholar
[4] Dade, E. C., Group-graded rings and modules. Math. Z. 174(1980), 241–262.Google Scholar
[5] Erdmann, K., Blocks and simple modules with cyclic vertices. Bull. London Math. Soc. 9(1977), 216–218.Google Scholar
[6] Knörr, R., On the vertices of irreducible modules. Ann.Math. 110(1979), 487–499.Google Scholar
[7] Landrock, P., Finite group algebras and their modules. Cambridge University Press, Cambridge, 1983.Google Scholar
[8] Landrock, P. and Michler, G. O., Block structure of the smallest Janko group. Math. Ann. 232(1978), 205–238.Google Scholar
[9] Marcus, A., Representation theory of group-graded algebras. Nova Science Publishers, Inc., Commack, New York, 1999.Google Scholar
[10] Okuyama, T., Module correspondence in finite groups. Hokkaido Math. J. 10(1981), 299–318.Google Scholar
[11] Sibley, D. A., Vertices, blocks and virtual characters. J. Algebra 132(1990), 501–507.Google Scholar
[12] Thévenaz, J., G-algebras and modular representation theory. Oxford University Press, Oxford, 1995.Google Scholar