Non-abelian tensor product and homology of Lie Superalgebras

Abstract

We introduce the non-abelian tensor product of Lie superalgebras, study some of its properties including nilpotency, solvability and Engel, and we use it to describe the universal central extensions of Lie superalgebras. We present the low-dimensional non-abelian homology of Lie superalgebras and establish its relationship with the cyclic homology of associative superalgebras. We also define the non-abelian exterior product and give an analogue of Miller's theorem, Hopf formula and a six-term exact sequence for the homology of Lie superalgebras.

References in corpus (2)

• Universal central extensions of $s{l}_{m|n}$ over $Z/2Z$-graded algebras
• Universal central extensions of $\mathfrak{sl}(m,n,A)$ of small rank over associative superalgebras

Cited by in corpus (8)

• HNN-extension of Lie superalgebras
• From Lie algebra crossed modules to tensor hierarchies
• On multipliers of pairs of Lie superalgebras
• On universal $\alpha$-central extensions of Hom-preLie algebras
• Detecting Capable Lie Superalgebra
• Universal central extensions of superdialgebras of matrices
• Capability and the Schur multiplier of generalized Heisenberg Lie superalgebras
• On $2$-Nilpotent Multiplier of Lie Superalgebras