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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Finite quaternionic matrix groups
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by Gabriele Nebe PDF
Represent. Theory 2 (1998), 106-223 Request permission

Abstract:

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.
References
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Additional Information
  • Gabriele Nebe
  • Affiliation: Lehrstuhl B für Mathematik, RWTH Aachen, Templergraben 64, 52062 Aachen, Germany
  • MR Author ID: 344248
  • Email: gabi@math.rwth-aachen.de
  • 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: https://doi.org/10.1090/S1088-4165-98-00011-9
  • MathSciNet review: 1615333