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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 $$A$$.

##### 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
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##### References:
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