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Strongly reversible classes in $\mathrm{SL}(n,\mathbb{C})$

Part of: Structure and classification of infinite or finite groups Basic linear algebra

Published online by Cambridge University Press:  30 April 2025

Krishnendu Gongopadhyay Open the ORCID record for Krishnendu Gongopadhyay [Opens in a new window] ,
Tejbir Lohan Open the ORCID record for Tejbir Lohan [Opens in a new window]  and
Chandan Maity Open the ORCID record for Chandan Maity [Opens in a new window]
Krishnendu Gongopadhyay*
Affiliation:
Department of Mathematical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Sector 81, S.A.S. Nagar, Knowledge City, Punjab 140306, India
Tejbir Lohan
Affiliation:
Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016, India
Chandan Maity
Affiliation:
Department of Mathematical Sciences, Indian Institute of Science Education and Research (IISER) Berhampur, Berhampur, Odisha 760003, India
*
Corresponding author: Krishnendu Gongopadhyay, email: [email protected]
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Abstract

An element of a group is called strongly reversible or strongly real if it can be expressed as a product of two involutions. We provide necessary and sufficient conditions for an element of $\mathrm{SL}(n,\mathbb{C})$ to be a product of two involutions. In particular, we classify the strongly reversible conjugacy classes in $\mathrm{SL}(n,\mathbb{C})$.

Keywords

reversibilitystrongly reversible elementsbireflectional elementsreversing symmetry groupJordan canonical formWeyr canonical form

MSC classification

Primary: 20E45: Conjugacy classes 15A23: Factorization of matrices
Secondary: 15A21: Canonical forms, reductions, classification 15A27: Commutativity
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , First View , pp. 1 - 32
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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