2007.234: Lie powers and Witt vectors

2007.234: R. M. Bryant and Marianne Johnson (2008) Lie powers and Witt vectors. Journal of Algebraic Combinatorics. ISSN 0925-9899

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DOI: 10.1007/s10801-007-0117-9

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 $V^{\otimes k}$.

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