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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Generic central extensions and projective representations of finite groups
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by Rachel Quinlan
Represent. Theory 5 (2001), 129-146
Published electronically: June 5, 2001


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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Bibliographic 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:
  • Received by editor(s): February 26, 2001
  • Received by editor(s) in revised form: March 23, 2001
  • Published electronically: June 5, 2001
  • © Copyright 2001 American Mathematical Society
  • Journal: Represent. Theory 5 (2001), 129-146
  • MSC (2000): Primary 20C25; Secondary 20C07
  • DOI:
  • MathSciNet review: 1835002