Congruences of convex algebras. (Q2341527)

A convex algebra is an algebra with an infinite set of operations of arbitrary positive arities providing convex combination of arguments, which satisfy two axiom schemes: the projection axiom scheme stating that a convex combination with a single coefficient equal to 1 is the identity map, and the barycenter axiom scheme stating that a convex combination of convex combinations equals the convex combination with suitably multiplied and summed coefficients. Examples of convex algebras are provided by convex subsets of a vector space. It is presented a full description of congruences on convex algebras. As a consequence of this description is obtained that finitely generated convex algebras are finitely presented. Similar results are obtained for positively or absolutely convex algebras.