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Matching simple modules of condensation algebras

Part of: Representation theory of groups

Published online by Cambridge University Press:  01 December 2012

Felix Noeske
Felix Noeske*
Affiliation:
Lehrstuhl D für Mathematik, RWTH Aachen University, 52056 Aachen, Germany (email: felix.noeske@math.rwth-aachen.de)

Abstract

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We revise the matching algorithm of Noeske (LMS J. Comput. Math. 11 (2008) 213–222) and introduce a new approach via composition series to expedite the calculations. Furthermore, we show how the matching algorithm may be applied in the more general and frequently occurring setting that we are only given subalgebras of the condensed algebras which each contain the separable algebra of one of their Wedderburn–Malcev decompositions.

MSC classification

Secondary: 20C40: Computational methods
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 15 , May 2012 , pp. 374 - 384
Copyright
© The Author(s) 2012

References

[1]Curtis, C. W. and Reiner, I., ‘Representation theory of finite groups and associative algebras’, Pure and Applied Mathematics, vol. XI (Interscience Publishers, a division of John Wiley & Sons, New York, London, 1962).Google Scholar
[2]Hiss, G., Müller, J., Noeske, F. and Thackray, J., ‘The Brauer characters of the sporadic simple Harada–Norton group and its automorphism group in characteristics 2 and 3’, LMS J. Comput. Math. 15 (2012) 257–280.CrossRefGoogle Scholar
[3]Holt, D. F., Eick, B. and O’Brien, E. A., Handbook of computational group theory, Discrete Mathematics and its Applications (Chapman & Hall/CRC, Boca Raton, FL, 2005).CrossRefGoogle Scholar
[4]Lux, K., ‘Algorithmic methods in modular representation theory’. http://math.arizona.edu/∼klux/habil.dvi.gz, 1997.Google Scholar
[5]Lux, K., Müller, J. and Ringe, M., ‘Peakword condensation and submodule lattices: an application of the MEAT-AXE’, J. Symbolic Comput. 17 (1994) no. 6, 529–544.CrossRefGoogle Scholar
[6]Lux, K., Neunhöffer, M. and Noeske, F., ‘Condensation of homomorphism spaces’, LMS J. Comput. Math. 15 (2012) 140–157.CrossRefGoogle Scholar
[7]Lux, K. and Wiegelmann, M., ‘Condensing tensor product modules’, The atlas of finite groups: ten years on (Birmingham, 1995), London Mathematical Society Lecture Note Series 249 (Cambridge University Press, Cambridge, 1998) 174–190.CrossRefGoogle Scholar
[8]Lux, K. and Wiegelmann, M., ‘Determination of socle series using the condensation method’, J. Symbolic Comput. 31 (2001) no. 1–2, 163–178; Computational algebra and number theory (Milwaukee, WI, 1996).CrossRefGoogle Scholar
[9] The modular atlas hompage. http://www.math.rwth-aachen.de/∼MOC/ .Google Scholar
[10]Noeske, F., ‘Tackling the generation problem in condensation’, J. Algebra 309 (2007) no. 2, 711–722.CrossRefGoogle Scholar
[11]Noeske, F., ‘Matching simple modules of condensed algebras’, LMS J. Comput. Math. 11 (2008) 213–222.CrossRefGoogle Scholar
[12]Ryba, A. J. E., ‘Computer condensation of modular representations’, J. Symbolic Comput. 9 (1990) no. 5–6, 591–600; Computational group theory, Part 1.CrossRefGoogle Scholar