The Automorphism Group of a Metropolis-Rota Implication Algebra

TL;DR

This paper investigates the automorphism group of MR-algebras, establishing its isomorphism with the inner automorphism group of a filter algebra through functorial generalizations.

Contribution

It introduces functors linking implication and cubic algebras, generalizes inner automorphisms, and characterizes the automorphism group of MR-algebras.

Findings

Automorphism group of MR-algebras is isomorphic to the inner automorphism group of a filter algebra.

Development of functors between implication and cubic algebras.

Generalization of the concept of inner automorphism.

Abstract

We discuss the group of automorphisms of a general MR-algebra. We develop several functors between implication algebras and cubic algebras. These allow us to generalize the notion of inner automorphism. We then show that this group is always isomorphic to the group of inner automorphisms of a filter algebra.