Module structure of the free Lie ring on three generators
Let Ln denote the homogeneous component of degree n in the free Lie ring on three generators, viewed as a module for the symmetric group S3 of all permutations of those generators. This paper gives a Krull-Schmidt Theorem for the Ln: if n > 1 and Ln is written as a direct sum of indecomposable submodules, then the summands come from four isomorphism classes, and explicit formulas for the number of summands from each isomorphism class show that these multiplicities are independent of the...[Show more]
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|Source:||Archiv der Mathematik|
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