The dimension of products of n homogeneous components in free lie algebras

Year 2019, Volume: 68 Issue: 2, 1774 - 1779, 01.08.2019

Nil Mansuroğlu

https://doi.org/10.31801/cfsuasmas.457500

Abstract

Let L be a free Lie algebra of finite rank r≥2 over a field F and we let L_{m_{i}} denote the degree m_{i} homogeneous component of L. Ralph Stöhr and Micheal Vaughan-Lee derived formulae for the dimension of the subspaces [L_{m₁},L_{m₂}] for all m₁ and m₂. Then, the author and R. Stöhr obtained formulae for the dimension of the products [L_{m₁},L_{m₂},L_{m₃}] under certain conditions on m₁,m₂,m₃. In this paper, we study on products of n homogeneous components in free Lie algebra and we derive formulae for the dimension of such products.

Keywords

Free Lie algebras, homogeneous component

References

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