2023/03/01 by Pazzis, Clément de Seguins
#15A23 #16W10 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2303.00820
A classical theorem of Wonenburger, Djokovic, Hoffmann and Paige states that an element of the general linear group of a finite-dimensional vector space is the product of two involutions if and only if it is similar to its inverse. We give a very elementary proof of this result when the underlying field \mathbbF is algebraically closed with characteristic other than 2. In that situation, the result is generalized to the group of invertibles of any finite-dimensional algebra over \mathbbF.