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Twisted group algebras and their representations

Published online by Cambridge University Press:  09 April 2009

S. B. Conlon
S. B. Conlon
Affiliation:
University of Sydney.
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Let be a finite group, a field. A twisted group algebra A() on over is an associative algebra whose elements are the formal linear combinations and in which the product (A)(B) is a non-zero multiple of (AB), where AB is the group product of A, B ∈: . One gets the ordinary group algebra () by taking each fA, B ≠ 1.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 4 , Issue 2 , May 1964 , pp. 152 - 173
Copyright
Copyright © Australian Mathematical Society 1964

References

[1]Artin, E., Nesbitt, C. J. and Thrall, R., Rings with minimum condition, Univ. of Michigan Press, Ann Arbor, 1955.Google Scholar
[2]Asano, K., Osima, M. and Takahasi, M., Über die Darstellung von Gruppen durch Kollineationen im Körper der Charakteristik p, Proc. Phys.-Math. Soc. Japan (3) 19 (1937), 199–209.Google Scholar
[3]Asano, K., and Shoda, K., Zur Theorie der Darstellungen einer endlichen Gruppe durch Kollineationen, Compositio Math. 2 (1935), 230–240.Google Scholar
[4]Brauer, R., Zur Darstellungstheorie der Gruppen endlicher Ordnung, Math. Z. 63 (1956), 406–444.Google Scholar
[5]Clifford, A. H., Representations induced in an invariant subgroup, Ann. of Math. (2) 38 (3) (1937), 533–550.Google Scholar
[6]Curtis, C. W. and Reiner, I., Representation theory of finite groups and associative algebras, Interscience, New York, 1962.Google Scholar
[7]Fitting, H., Die Theorie der Automorphismenringe Abelscher Gruppen und ihr Analogon bei nicht kommutativen Gruppen, Math. Ann. 107 (4) (1932), 514–542.CrossRefGoogle Scholar
[8]Green, J. A., On the indecomposable representations of a finite group, Math. Z. 70 (1959), 430–445.Google Scholar
[9]Higman, D. G., Modules with a group of operators, Duke Math. J. 21 (1954), 369–376.Google Scholar
[10]Higman, D. G., Indecomposable representations at characteristic p, Duke Math. J. 21 (1954), 377–381.Google Scholar
[11]Higman, D. G., Relative cohomology, Canad. J. Math. 9 (1957), 19–34.CrossRefGoogle Scholar
[12]Hochschild, G., Relative homological algebra, Trans. Amer. Math. Soc. 82 (1956), 246–269.CrossRefGoogle Scholar
[13]Jacobson, N., The Theory of Rings (Mathematical Surveys, number II), Amer. Math. Soc., 1943.Google Scholar
[14]Kleppner, A., The structure of some induced representations, Duke Math. J. 29 (4) (1962), 555–572.Google Scholar
[15]Nakayama, T., Some studies on regular representations, induced representations and modular representations, Ann. of Math. (2) 39 (2) (1938), 361–369.Google Scholar
[16]Rosenberg, A., Blocks and centres of group algebras, Math. Z. 76 (1961), 209–216.CrossRefGoogle Scholar
[17]Schur, J., Über die Darstellung der endlichen Gruppen durch gebrochene lineare Substitutionen, J. Reine Angew. Math., 127 (1) (1904), 20–55.Google Scholar
[18]Schur, J., Untersuchungen über die Darstellung der endlichen Gruppen durch gebrochene lineare Substitutionen, J. Reine Angew. Math., 132 (2) (1907), 85–137.Google Scholar
[19]Srinivasan, B., On the indecomposable representations of a certain class of groups, Proc. London Math. Soc. (3) 10 (1960), 497–513.CrossRefGoogle Scholar
[20]Tazawa, M., Über die Darstellung der endlichen verallgemeinerten Gruppen, Sci. Rep. Tohoku Univ. (1) 23 (1934), 76–88.Google Scholar
[21]Tucker, P. A., On the reduction of induced representations of finite groups, Amer. J. Math. 84 (3) (1962), 400–420.CrossRefGoogle Scholar