Conjugate Real Classes in General Linear Groups

Krishnendu Gongopadhyay; Sudip Mazumder; Sujit Kumar Sardar

Conjugate Real Classes in General Linear Groups

Rings and Algebras 2018-01-19 v3

Authors: Krishnendu Gongopadhyay , Sudip Mazumder , Sujit Kumar Sardar

Abstract

Let $\F$ be a field with a non-trivial involution $c: \alpha \to \alpha^c$ . An element $g \in {\rm GL}_n(\F)$ is called $c$ -real if it is conjugate to $(g^c)^{-1}$ . We prove that for $n \geq 2$ , $g \in {\rm GL}_n(\F)$ is $c$ -real if and only if it has a representation in some unitary group of degree $n$ over $\F$ .

Keywords

conjugacy classes in groups

Cite

@article{arxiv.1702.08149,
  title  = {Conjugate Real Classes in General Linear Groups},
  author = {Krishnendu Gongopadhyay and Sudip Mazumder and Sujit Kumar Sardar},
  journal= {arXiv preprint arXiv:1702.08149},
  year   = {2018}
}

Comments

minor revision. Fixed minor errors

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