Finite Integral Relation Algebras
نویسنده
چکیده
The method of forming complex algebras of finite ternary relations will produce all finite nonassociative relation algebras. We use this method to construct many interesting algebras. Every atomic NA determines an involution on atoms, which in turn determines both the cycles of the algebra and also the missing, or forbidden cycles. So we begin by studying the cycles of an arbitrary involution. Suppose ̆ is an involution on U , that is, ̆ : U → U and ̆̆ u = u for all u ∈ U . For any x, y, z ∈ U let
منابع مشابه
BCK-ALGEBRAS AND HYPER BCK-ALGEBRAS INDUCED BY A DETERMINISTIC FINITE AUTOMATON
In this note first we define a BCK‐algebra on the states of a deterministic finite automaton. Then we show that it is a BCK‐algebra with condition (S) and also it is a positive implicative BCK‐algebra. Then we find some quotient BCK‐algebras of it. After that we introduce a hyper BCK‐algebra on the set of all equivalence classes of an equivalence relation on the states of a deterministic finite...
متن کاملIntegral forms in vertex operator algebras which are invariant under finite groups
For certain vertex operator algebras (e.g., lattice type) and given finite group of automorphisms, we prove existence of a positive definite integral form invariant under the group. Applications include an integral form in the Moonshine VOA which is invariant under the Monster, and examples in other lattice type VOAs.
متن کاملGames in algebraic logic: axiomatisations and beyond
Outline 1. Algebras of relations: a quick introduction to relation algebras, representable relation algebras 2. Case study: atomic and finite relation algebras • atom structures; representations of finite relation algebras • two examples: McKenzie’s algebra; the so-called ‘anti-Monk algebra’ 3. Games to characterise representability: the games, axioms from games, examples 4. Infinite relation a...
متن کاملAspects of relation algebras
Outline 1. Introduction to relation algebras. Representations. Atom structures. Examples. 2. Using games to build representations. Axiomatising the finite representable relation algebras. 3. 'Rainbow' construction (Hirsch). Monk's theorem that the representable relation algebras are not finitely axiomatisable. 4. Relativised representations. Weakly associative algebras (WA, Maddux). Finite base...
متن کامل