UC Berkeley

Let V be a variety of not necessarily associative algebras, and A an inverse limit of nilpotent algebras Ai ∈ V, such that some finitely generated subalgebra S ⊆ A is dense in A under the inverse limit of the discrete topologies on the Ai. A sufficient condition on V is obtained for all algebra homomorphisms from A to finite-dimensional algebras B to be continuous; in other words, for the kernels of all such homomorphisms to be open ideals. This condition is satisfied, in particular, if V is the variety of associative, Lie, or Jordan algebras. Examples are given showing the need for our hypotheses, and some open questions are noted. 2013 © University of Illinois.