Berezinian of supermatrices and universal recurrence relations for exterior powers
The Berezinian is the analog of the determinant in the Z_2-graded situation. It is a rational invariant of supermatrices. We study expansions of the charactersitic function Ber(1+zA) of a linear operator on a superspace, and deduce universal recurrence relations satisfied by supertraces of exterior powers of A. There are underlying recurrence relations in the Grothendieck ring. We obtain a new formula for the Berezinian expressing it as a rational function of polynomial invariants (a ratio of two Hankel determinants built of supertraces). We elucidate the Hamilton-Cayley theorem for the super case.
(Based on joint work with Hovhannes Khudaverdian.)