Linear Conjugacy. Issue 4 (December 2019)

• Record Type: Journal Article
• Authors: Steinberg, Benjamin
• Is Part Of: Canadian mathematical bulletin =. Volume 62:Issue 4(2019)
• Page Start: 886
• Page End: 895
• Publication Date: 2019-12
• Subjects: 20M30; monoid, -- representation theory, -- conjugacy; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.4153/S0008439519000031
• Languages: English
• ISSNs: 0008-4395

Abstract

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 $\Bbbk$ .