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On metric Leibniz algebras and deformations. (English) Zbl 1485.17008

Summary: In this note, we consider low-dimensional metric Leibniz algebras with an invariant inner product over the complex numbers up to dimension 5. We study their deformations, and give explicit formulas for the cocycles and deformations. We identify among those the metric deformations.

MSC:

17A32 Leibniz algebras
17B05 Structure theory for Lie algebras and superalgebras
17B30 Solvable, nilpotent (super)algebras
17A60 Structure theory for nonassociative algebras
17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras
17B55 Homological methods in Lie (super)algebras
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References:

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