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A non-abelian tensor product of Lie algebras. (English) Zbl 0724.17016
Let M and N be Lie algebras acting compatibly on one another. The author constructs a “non-abelian tensor product” \(M\otimes N\); it is a quotient of the usual tensor product over the ground ring, and it takes account of the actions. For a single Lie algebra P, the author also constructs an exterior square \(P\bigwedge P\) as a quotient of \(P\otimes P\). He gives various properties of these constructions, especially connections with homology groups. The work is motivated by similar constructions in group theory [R. Brown and J.-L. Loday, Topology 26, 311-335 (1987; Zbl 0622.55009)].

MSC:
17B55 Homological methods in Lie (super)algebras
55Q05 Homotopy groups, general; sets of homotopy classes
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