Reversibility of Affine Transformations

2022/11/21 by Krishnendu Gongopadhyay, Gongopadhyay, Krishnendu, Tejbir Lohan +3 · 1 citation
Mathematics · #15B33 (Secondary) [2020] #32M17 #53A15 (Primary) 20E45 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2211.11606

openalex publication_date 2022/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

An element g in a group G is called reversible if g is conjugate to g^-1 in G . An element g in G is strongly reversible if g is conjugate to g^-1 by an involution in G. The group of affine transformations of \mathbbDⁿ may be identified with the semi-direct product GL(n, \mathbbD) \ltimes \mathbbDⁿ , where \mathbbD:=ℝ, ℂ or ℍ . This paper classifies reversible and strongly reversible elements in the affine group GL(n, \mathbbD) \ltimes \mathbbDⁿ .

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