# Denominator identities for the periplectic Lie superalgebra

## TL;DR

This paper establishes denominator identities for the periplectic Lie superalgebra, completing the set of such identities for all simple classical finite-dimensional Lie superalgebras, which is a significant theoretical advancement.

## Contribution

It provides the first proof of denominator identities specifically for the periplectic Lie superalgebra, filling a key gap in the theory of Lie superalgebras.

## Key findings

- Denominator identities for $rak{p}(n)$ are proven.
- Completes the classification of denominator identities for all simple classical finite-dimensional Lie superalgebras.
- Advances understanding of the structure of periplectic Lie superalgebras.

## Abstract

We prove denominator identities for the periplectic Lie superalgebra $\mathfrak{p}(n)$, thereby completing the problem of finding denominator identities for all simple classical finite-dimensional Lie superalgebras.