On the module structure of free Lie algebras

Bryant, R.; Stöhr, Ralph

doi:10.1090/S0002-9947-99-02369-7

On the module structure of free Lie algebras
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by R. M. Bryant and Ralph Stöhr PDF

Trans. Amer. Math. Soc. 352 (2000), 901-934 Request permission

Abstract:

We study the free Lie algebra $L$ over a field of non-zero characteristic $p$ as a module for the cyclic group of order $p$ acting on $L$ by cyclically permuting the elements of a free generating set. Our main result is a complete decomposition of $L$ as a direct sum of indecomposable modules.

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