The Algebra of Filters of a Cubic Algebra

Abstract

In this paper we discuss the inclusion ordering on the filters of a filter algebra, a special type of Metropolis-Rota algeba. Using embeddings into interval algebras we show that the notion of "untwisted" gives rise to a congruence relation on the group of g-filters. We also show that there is a natural reflection operator on the class of filters with an easily definable enveloping cubic subalgebra.