  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.
