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Matching Simple Modules of Condensed Algebras

Published online by Cambridge University Press:  01 February 2010

Felix Noeske
Felix Noeske
Affiliation:
Lehrstuhl D für Mathematik, RWTH Aachen University, 52056 Aachen, Germany, Felix.Noeske@math.rwth-aachen.de

Abstract

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Let A be a finite dimensional algebra over a finite field F. Condensing an A-module V with two different idempotents e and e′ leads to the problem that to compare the composition series of V e and V e′, we need to match the composition factors of both modules. In other words, given a composition factor S of V e, we have to find a composition factor S′ of V e′ such that there exists a composition factor Ŝ of V with Ŝ e ≅ S and Ŝ e′ ≅ S′, or prove that no such S′ exists. In this note, we present a computationally tractable solution to this problem.

Information

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 11 , 2008 , pp. 213 - 222
Copyright
Copyright © London Mathematical Society 2008

References

1.‘The Modular Atlas Homepage’, www.math.rwth-aachen.de/~MOC/.Google Scholar
2.Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A., Atlas of finite groups. Maximal subgroups and ordinary characters for simple groups. With computational assistance from J. G. Thackray (Oxford University Press, Eynsham, 1985). ISBN 0-19-853199-0.Google Scholar
3.Green, J. A., Polynomial representations of GLn, Lecture Notes in Mathematics 830 (Springer, Berlin, 1980). ISBN 3-540-10258-2.Google Scholar
4.Hiss, G., Neunhöffer, M. and Noeske, F., ‘The 2-modular characters of the Fischer group Fi23’, J. Algebra 300 (2006) 555–570.CrossRefGoogle Scholar
5.Lübeck, F. and Neunhöffer, M., ‘Enumerating large orbits and direct condensation’, Experiment. Math. 10 (2001) 197–205.CrossRefGoogle Scholar
6.Lux, K., Müller, J. and Ringe, M., ‘Peakword condensation and submodule lattices: an application of the MEAT-AXE’, J. Symbolic Gomput. 17 (1994) 529–544.CrossRefGoogle Scholar
7.Lux, K., Neunhöffer, M. and Noeske, F., ‘Condensation of homomorphism spaces’, in preparation.Google Scholar
8.Lux, K. and Wiegelmann, M., ‘Condensing tensor product modules’, The atlas of finite groups: ten years on, Birmingham, 1995, London Math. Soc. Lecture Note Ser. 249 (Cambridge Univ. Press, Cambridge, 1998) 174–190.CrossRefGoogle Scholar
9.Lux, K. and Wiegelmann, M., ‘Determination of socle series using the condensation method’, Computational algebra and number theory, Milwaukee, WI, 1996, J. Symbolic Gomput. 31 (2001) 163–178.Google Scholar
10.Müller, J. and Rosenboom, J., ‘Condensation of induced representations and an application: the 2-modular decomposition numbers of Co2’, Computational methods for representations of groups and algebras, Essen, 1997, Progr. Math. 173 (Birkhäuser, Basel, 1999) 309–321.Google Scholar
11.Noeske, F., ‘Morita-Äquivalenzen in der algorithmischen Darstellungstheorie’, PhD thesis, RWTH Aachen University, 2005.Google Scholar
12.Noeske, F., ‘The 2- and 3-modular characters of the sporadic simple Fischer group Fi22 and its cover’, J. Algebra 309 (2007) 723–743.CrossRefGoogle Scholar
13.Parker, R. A., ‘The computer calculation of modular characters (the Meat-Axe)’, Computational group theory, Durham, 1982 (Academic Press, London, 1984) 267–274.Google Scholar
14.Ryba, A. J. E., ‘Computer condensation of modular representations. Computational group theory, Part 1, J. Symbolic Comput. 9 (1990) 591–600.CrossRefGoogle Scholar
15.Ryba, A. J. E., ‘Condensation of symmetrized tensor powers’, J. Symbolic Comput. 32 (2001) 273–289.CrossRefGoogle Scholar