Totally decomposable algebras with involution and R-triviality
M. Archita, Karim Johannes Becher
TL;DR
This paper proves that the group of proper projective similitudes of a totally decomposable algebra with involution of the first kind over a field with characteristic not 2 is R-trivial, advancing understanding of algebraic group properties.
Contribution
It establishes R-triviality for the group of proper projective similitudes in a specific class of algebras with involution, a new result in algebraic group theory.
Findings
Group of proper projective similitudes is R-trivial
Applicable to totally decomposable algebras with involution of the first kind
Field characteristic is not 2
Abstract
We show that the group of proper projective similitudes of a totally decomposable algebra with involution of the first kind over a field of characteristic different from 2 is R-trivial.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Finite Group Theory Research