Abstract
Suppose that L is the free Lie algebra generated by k elements. This is a homogeneous algebra and the dimensions of its homogeneous components are given by Witt's formula dimL n= 1 n ∑ a|nμ(a)k n/a , where μ( n) is the Möbius function. Recently the author discovered generating functions for the whole of the free Lie superalgebra. These series yield some new dimension formulas. Now we present generating functions for the free Lie p-algebras. As a corollary, we suggest dimension formulas similar to Witt's formula.
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