R-triviality for adjoint classical groups of type C

TL;DR

This paper investigates R-triviality of the projective similitude group associated with symplectic involutions on central simple algebras, establishing new cases where R-triviality holds.

Contribution

It extends the understanding of R-triviality for adjoint classical groups of type C by identifying two new cases where PSim(A,s) is R-trivial.

Findings

PSim(A,s) is R-trivial in two new cases

Advances the classification of R-trivial adjoint classical groups

Provides new insights into symplectic involutions on central simple algebras

Abstract

For a central simple algebra with a symplectic involution (A,s) over a field of characteristic different from 2, we show that its group of projective similitudes PSim(A,s) is R-trivial in two new cases.