Linear Conjugacy
Canadian mathematical bulletin, Tome 62 (2019) no. 4, pp. 886-895
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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 $\Bbbk$.
Steinberg, Benjamin. Linear Conjugacy. Canadian mathematical bulletin, Tome 62 (2019) no. 4, pp. 886-895. doi: 10.4153/S0008439519000031
@article{10_4153_S0008439519000031,
author = {Steinberg, Benjamin},
title = {Linear {Conjugacy}},
journal = {Canadian mathematical bulletin},
pages = {886--895},
year = {2019},
volume = {62},
number = {4},
doi = {10.4153/S0008439519000031},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000031/}
}
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