Second homology of generalized periplectic Lie superalgebras

Let (R,−) be an arbitrary unital associative superalgebra with superinvolution over a commutative ring k with 2 invertible. The second homology of the generalized periplectic Lie superalgebra pm(R,−) for m⩾3 has been completely determined via an explicit construction of its universal central extension. In particular, this second homology is identified with the first Z/2Z-graded dihedral homology of R with certain superinvolution whenever m⩾5.