Centers of cyclotomic Sergeev superalgebras

TL;DR

This paper characterizes the center of cyclotomic Sergeev superalgebras of odd level, showing it is generated by symmetric functions in the squares of polynomial generators, via a surjective map from the affine superalgebra.

Contribution

It establishes the surjectivity of the natural map from the affine Sergeev superalgebra's center to the even center of cyclotomic Sergeev superalgebras of odd level, clarifying their structure.

Findings

The even center is generated by symmetric functions in polynomial squares.

The map from the affine to cyclotomic superalgebra centers is surjective.

The structure of the center is explicitly described for odd level cases.

Abstract

We prove that the natural map from the center of the affine Sergeev superalgebra to the even center of any cyclotomic Sergeev superalgebra of odd level is surjective, hence that the even center of a cyclotomic Sergeev superalgebra of odd level consists of symmetric functions in the squares of its polynomial generators.