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Linear Conjugacy

Part of: Semigroups

Published online by Cambridge University Press:  29 January 2019

Benjamin Steinberg
Benjamin Steinberg*
Affiliation:
Department of Mathematics, City College of New York, Convent Avenue at 138th Street, New York, New York 10031, USA Email: bsteinberg@ccny.cuny.edu
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Abstract

We say that two elements of a group or semigroup are $\Bbbk$-linear conjugates if their images under any linear representation over $\Bbbk$ are conjugate matrices. In this paper we characterize $\Bbbk$-linear conjugacy for finite semigroups (and, in particular, for finite groups) over an arbitrary field $\Bbbk$.

Keywords

monoidrepresentation theoryconjugacy

MSC classification

Primary: 20M30: Representation of semigroups; actions of semigroups on sets
Type
Article
Information
Canadian Mathematical Bulletin , Volume 62 , Issue 4 , December 2019 , pp. 886 - 895
Copyright
© Canadian Mathematical Society 2019 

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Footnotes

This work was partially supported by grants from the Simons Foundation (#245268), the Binational Science Foundation of Israel and the U.S.A. (#2012080) by a CUNY Collaborative Incentive Research Grant, by NSA MSP #H98230-16-1-0047 and by a Fulbright Scholar award.

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