Second N=1 Superanalog of Complex Structure

Abstract

We found another N=1 odd superanalog of complex structure (the even one is widely used in the theory of super Riemann surfaces). New N=1 superconformal-like transformations are similar to anti-holomorphic ones of nonsupersymmetric complex function theory. They are dual to the ordinary superconformal transformations subject to the Berezinian addition formula presented, noninvertible, highly degenerated and twist parity of the tangent space in the standard basis. They also lead to the ''mixed cocycle condition'' which can be used in building noninvertible objects analogous to super Riemann surfaces. A new parametrization for the superconformal group is presented which allows us to extend it to a semigroup and to unify the description of old and new transformations.