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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.


Finite quaternionic matrix groups
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by Gabriele Nebe
Represent. Theory 2 (1998), 106-223
Published electronically: April 10, 1998


Let $\mathcal {D}$ be a definite quaternion algebra such that its center has degree $d$ over $\mathbb {Q}$. A subgroup $G$ of $GL_n(\mathcal {D})$ is absolutely irreducible if the $\mathbb {Q}$-algebra spanned by the matrices in $G$ is $\mathcal {D}^{n\times n}$. The finite absolutely irreducible subgroups of $GL_n(\mathcal {D})$ are classified for $nd \leq 10$ by constructing representatives of the conjugacy classes of the maximal finite ones. Methods to construct the groups and to deal with the quaternion algebras are developed. The investigation of the invariant rational lattices yields quaternionic structures for many interesting lattices.
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Bibliographic Information
  • Gabriele Nebe
  • Affiliation: Lehrstuhl B für Mathematik, RWTH Aachen, Templergraben 64, 52062 Aachen, Germany
  • MR Author ID: 344248
  • Email:
  • Received by editor(s): December 23, 1996
  • Received by editor(s) in revised form: February 3, 1998, and February 16, 1998
  • Published electronically: April 10, 1998
  • © Copyright 1998 American Mathematical Society
  • Journal: Represent. Theory 2 (1998), 106-223
  • MSC (1991): Primary 20C10, 11E39, 11R52
  • DOI:
  • MathSciNet review: 1615333