# Lie powers and Witt vectors

Bryant, R. M. and Johnson, Marianne (2008) Lie powers and Witt vectors. Journal of Algebraic Combinatorics. ISSN 0925-9899 (In Press)

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## Abstract

In the study of Lie powers of a module $V$ in prime characteristic $p$, a basic role is played by certain modules $B_n$ introduced by Bryant and Schocker. The isomorphism types of the $B_n$ are not fully understood, but these modules fall into infinite families $\{ B_k, B_{pk}, B_{p^2 k}, \dots \}$, one family $B(k)$ for each positive integer $k$ not divisible by $p$, and there is a recursive formula for the modules within $B(k)$. Here we use combinatorial methods and Witt vectors to show that each module in $B(k)$ is isomorphic to a direct sum of tensor products of direct summands of the $k$th tensor power $V^{\otimes k}$.

Item Type: Article The original publication is available at www.springerlink.com/ Free Lie algebra, Lie power, Tensor power, Witt vector MSC 2010, the AMS's Mathematics Subject Classification > 11 Number theoryMSC 2010, the AMS's Mathematics Subject Classification > 17 Nonassociative rings and algebrasMSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations Dr Marianne Johnson 30 Dec 2007 20 Oct 2017 14:12 http://eprints.maths.manchester.ac.uk/id/eprint/1004

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