A non-abelian tensor product of Leibniz algebras. (English) Zbl 0936.17004

Gnedbaye, Allahtan V.

Ann. Inst. Fourier 49, No. 4, 1149-1177 (1999).

Let \({\mathfrak M}\) and \({\mathfrak N}\) be crossed Lie \({\mathfrak g}\)-algebras. D. Guin [Ann. Inst. Fourier 45, No. 1, 93-118 (1995; Zbl 0818.17022)] used the derivation functor \(\text{Der}_{\mathfrak g}({\mathfrak N},-)\) and its right adjoint, the non-abelian tensor product \(-\otimes_{\mathfrak g}{\mathfrak N}\) to construct a non-abelian (co)homology theory.
The aim of the paper is to extend these methods and results on Leibniz algebras – a non-commutative variation of Lie algebras. The author compares the Milnor-type Hochschild homology \(HH^M_\ast(A)\) and the classical Hochschild homology \(HH_\ast(A)\) of an associative algebra \(A\).

Reviewer: M.Golasiński (Toruń)

MSC:

17A32	Leibniz algebras
18G50	Nonabelian homological algebra (category-theoretic aspects)
16E40	(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)
17B55	Homological methods in Lie (super)algebras
17B56	Cohomology of Lie (super)algebras

Keywords:

Milnor-type Hochschild homology; crossed module; Leibniz algebra; non-abelian Leibniz (co)homology; non-abelian tensor product

References:

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