Hodge operators and groups of isometries of diagonalizable symmetric bilinear forms in characteristic two

TL;DR

This paper investigates the structure of isometry groups of symmetric bilinear forms in characteristic two and their actions on exterior powers, revealing new algebraic properties related to Hodge operators.

Contribution

It introduces a detailed analysis of isometry groups for non-alternating symmetric bilinear forms in characteristic two and explores their actions via Hodge operators.

Findings

Characterization of isometry groups in characteristic two

Analysis of group actions on exterior powers

Connections between Hodge operators and symmetry groups

Abstract

We study groups of isometries on non-alternating symmetric bilinear forms on vector spaces of characteristic two, and actions of these groups on exterior powers of the space, viewed as modules over algebras generated by Hodge operators.