Reversible Quaternionic Hyperbolic Isometries

2019/03/10 by Bhunia, Sushil, Gongopadhyay, Krishnendu · 1 citation
#20E45 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Primary 51M10 #Secondary 15B33

paper · doi:10.48550/arxiv.1903.04034

Abstract

Let G be a group. An element g in G is called reversible if it is conjugate to g^-1 within G, and called strongly reversible if it is conjugate to its inverse by an order two element of G. Let H_{\mathbb H}ⁿ be the n-dimensional quaternionic hyperbolic space. Let PSp(n,1) be the isometry group of H_{\mathbb H}ⁿ. In this paper, we classify reversible and strongly reversible elements in Sp(n) and Sp(n,1). Also, we prove that all the elements of PSp(n,1) are strongly reversible.

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• Strongly Doubly Reversible Pairs in Quaternionic Unitary Group of Signature (n,1)

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