# An analogue of the Perelomov-Popov formula for the Lie superalgebra Q(N)

## TL;DR

This paper derives an analogue of the Perelomov-Popov formula for the center of the universal enveloping algebra of the Lie superalgebra Q(N), linking central characters to highest weight parameters.

## Contribution

It provides a new formula connecting central elements and highest weight parameters for the Lie superalgebra Q(N), extending classical results to the superalgebra context.

## Key findings

- Derived an explicit formula for the center of the universal enveloping algebra of Q(N)
- Expressed central characters in terms of highest weight parameters
- Extended classical formulas to the superalgebra setting

## Abstract

In this short note we study the center of the universal enveloping algebra of the strange Lie superalgebra Q(N). We obtain an analogue of the well known Perelomov-Popov formula (1968) for central elements of this algebra - an expression of the central characters through the highest weight parameters.