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

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
Full Text: DOI Numdam EuDML
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