ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 17, 46, 47 Ekhaguere, G. O. S., Department of Mathematics, University of Ibadan, Ibadan, Nigeria Algebraic representation theory of partial algebras Let (A, Γ, ∘) be a partial algebra, i. e. A is a linear space, Γ ⊆ A × A is a relation on A and ∘ is a partial multiplication on A such that

(i) (x, y) ∈ Γ ⟺ x ∘ y ∈ A

(ii) (x, z) ∈ Γ and (y, z) ∈ Γ imply (αx + βy, z) ∈ Γ, and then (αx + βy) ∘ z = α(x ∘ z) + β(y ∘ z) for all α, β ∈ lC, the complex plane.

This paper develops the algebraic representation theory for partial algebras. We introduce the notion of irreducibility for representations of a partial algebra, prove necessary and sufficient conditions for a representation to be (a) irreducible or (b) completely reducible, and develop aspects of the decomposition theory of completely reducible representations.