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Journal of Lie Theory 29 (2019), No. 3, 611--618
Copyright Heldermann Verlag 2019

A Poincaré-Birkhoff-Witt Theorem for Profinite Pronilpotent Lie Algebras

Alastair Hamilton
Dept. of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, U.S.A.

We prove a version of the Poincaré-Birkhoff-Witt Theorem for profinite pronilpotent Lie algebras in which their symmetric and universal enveloping algebras are replaced with appropriate formal analogues and discuss some immediate corollaries of this result.

Keywords: Poincaré-Birkhoff-Witt, pronilpotent Lie algebra, formal power series, infinite-dimensional Lie algebra, profinite vector space.

MSC: 13J05, 13J10, 16S10, 16W70, 17B01, 17B35, 17B65.

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