Hovhannes Khudaverdian (University of Manchester)
khudian@manchester.ac.uk
In this talk we discuss relations between Berezinians (superdeterminants) of linear operators on Z2 - graded spaces and rational functions. Many interesting properties of Berezinians are revealed in this way.
As an application of these relations we consider a new algebraic notion of a p|q-homomorphism between commutative algebras.
The famous Gelfand-Kolmogorov theorem identifies the points of a compact Hausdorff space X with the ring homomorphisms from the algebra of continuous functions C(X) to the field of real numbers. Buchstaber and Rees obtained a similar description for any symmetric power Symn(X) using their notion of n-homomorphisms. Our construction leads to new notions of "generalized symmetric powers" Symp|q (X) and Sp|q (A) for a topological space and a commutative algebra.
The talk is based on joint works with Ted Voronov.