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Cyclic group representations for relation algebras $57_{65}$ and $63_{65}$

Jeremy F. Alm

Abstract

We exhibit finite cyclic group representations for relation algebras $57_{65}$ and $63_{65}$. As a consequence, of the ten symmetric integral RAs on four atoms having at least one flexible atom, all are now known to have a representation over a finite cyclic group except for $33_{65}$, which is not even known to be finitely representable.

Cyclic group representations for relation algebras $57_{65}$ and $63_{65}$

Abstract

We exhibit finite cyclic group representations for relation algebras and . As a consequence, of the ten symmetric integral RAs on four atoms having at least one flexible atom, all are now known to have a representation over a finite cyclic group except for , which is not even known to be finitely representable.

Paper Structure

This paper contains 4 sections, 2 equations, 1 table.

Table of Contents

  1. Introduction
  2. Cyclic Representations
  3. Conclusion
  4. Declarations