Research ArticleNo Access

Chain level proof for the isomorphism between Lie and Hochschild homologies

Zuhier Altawallbeh

Department of Mathematics, Tafila Technical University, Tafila 66110, Jordan

E-mail Address: zuhier1980@gmail.com

https://doi.org/10.1142/S1793557121501138Cited by:0 (Source: Crossref)

Abstract

In this paper, we prove the commutativity of the square in the chain level of both Chevalley Eilenberg complex of Lie homology and Hochschild complex, where the antisymmetrization map is used between the complexes. Originally, Loday proved this isomorphism by constructing a certain map satisfying relations of a presimplicial homotopy to prove the commutativity of the square mentioned above. Here, we present a different approach for the proof of the commutativity without constructing that certain map satisfying the relations of the presimplicial homotopy.

Communicated by L. A. Bokut

Keywords:

AMSC: 16E40, 18G60, 13D03, 17A32, 17B35

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