Open Access
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


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.


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George M. Bergman. "Continuity of homomorphisms on pro-nilpotent algebras." Illinois J. Math. 55 (3) 749 - 770, Fall 2011.


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

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

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

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

Vol.55 • No. 3 • Fall 2011
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