Finite dimensional factor algebras of F_2[X_1,...,X_n] and their fixed point subalgebras

TL;DR

This paper fully characterizes the fixed point subalgebras of finite dimensional factor algebras derived from polynomial algebras over the finite field F_2, with respect to all algebra automorphisms.

Contribution

It provides a complete description of fixed point subalgebras in a specific algebraic setting over F_2, extending understanding of automorphism-invariant substructures.

Findings

Complete classification of fixed point subalgebras

Description of automorphism groups involved

Insights into algebraic structure over finite fields

Abstract

Fixed point subalgebras of finite dimensional factor algebras of algebras of polynomials in n indeterminates over the finite field $\mathbb F_2$ (with respect to all $\mathbb F_2$-algebra automorphisms) are fully described.