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Representation Theory

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Generic central extensions and projective representations of finite groups


Author: Rachel Quinlan
Journal: Represent. Theory 5 (2001), 129-146
MSC (2000): Primary 20C25; Secondary 20C07
DOI: https://doi.org/10.1090/S1088-4165-01-00122-4
Published electronically: June 5, 2001
MathSciNet review: 1835002
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Abstract:

Any free presentation for the finite group $G$ determines a central extension $(R,F)$ for $G$ having the projective lifting property for $G$ over any field $k$. The irreducible representations of $F$ which arise as lifts of irreducible projective representations of $G$ are investigated by considering the structure of the group algebra $kF$, which is greatly influenced by the fact that the set of torsion elements of $F$ is equal to its commutator subgroup and, in particular, is finite. A correspondence between projective equivalence classes of absolutely irreducible projective representations of $G$ and $F$-orbits of absolutely irreducible characters of $F'$ is established and employed in a discussion of realizability of projective representations over small fields.


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Additional Information

Rachel Quinlan
Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1
Address at time of publication: Department of Mathematics, University College Dublin, Dublin, Ireland
Email: rachel.quinlan@ucd.ie

DOI: https://doi.org/10.1090/S1088-4165-01-00122-4
Received by editor(s): February 26, 2001
Received by editor(s) in revised form: March 23, 2001
Published electronically: June 5, 2001
Article copyright: © Copyright 2001 American Mathematical Society