Conjugate Real Classes in General Linear Groups

2017/02/27 by Gongopadhyay, Krishnendu, Mazumder, Sudip, Sardar, Sujit Kumar · 2 citations
#15A04 #FOS: Mathematics #Primary 20E45 #Rings and Algebras (math.RA) #Secondary 20G15

paper · doi:10.48550/arxiv.1702.08149

Abstract

Let \F be a field with a non-trivial involution c: α→ α^c. An element g ∈ \rm GL_n(\F) is called c-real if it is conjugate to (g^c)^-1. We prove that for n ≥ 2, g ∈ \rm GL_n(\F) is c-real if and only if it has a representation in some unitary group of degree n over \F.

Cited by

• Conjugate reversibility in complex special linear groups
• Kulkarni limit sets for cyclic quaternionic projective groups

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