Translator Disclaimer
Fall 2011 Continuity of homomorphisms on pro-nilpotent algebras
George M. Bergman
Illinois J. Math. 55(3): 749-770 (Fall 2011). DOI: 10.1215/ijm/1369841783

Abstract

Let $\mathbf{V}$ be a variety of not necessarily associative algebras, and $A$ an inverse limit of nilpotent algebras $A_i\in\mathbf{V}$, such that some finitely generated subalgebra $S\subseteq A$ is dense in $A$ under the inverse limit of the discrete topologies on the $A_i$.

A sufficient condition on $\mathbf{V}$ 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 $\mathbf{V}$ is the variety of associative, Lie, or Jordan algebras.

Examples are given showing the need for our hypotheses, and some open questions are noted.

Citation

Download Citation

George M. Bergman. "Continuity of homomorphisms on pro-nilpotent algebras." Illinois J. Math. 55 (3) 749 - 770, Fall 2011. https://doi.org/10.1215/ijm/1369841783

Information

Published: Fall 2011
First available in Project Euclid: 29 May 2013

zbMATH: 1285.17002
MathSciNet: MR3069282
Digital Object Identifier: 10.1215/ijm/1369841783

Subjects:
Primary: 17A01, 18A30, 49S10
Secondary: 16W80, 17B99, 17C99

Rights: Copyright © 2011 University of Illinois at Urbana-Champaign

JOURNAL ARTICLE
22 PAGES


SHARE
Vol.55 • No. 3 • Fall 2011
Back to Top