# Supertraces on queerified algebras

## TL;DR

This paper characterizes supertraces on various queerified algebras, including matrix, Calogero-Moser, higher spin, and pseudo-differential operator algebras, revealing integrability properties of related Euler equations.

## Contribution

It provides a comprehensive description of supertraces on queerified algebras, linking algebraic structures to integrability of associated dynamical systems.

## Key findings

- Supertraces are explicitly described for queerified matrix and Calogero-Moser algebras.
- Supertraces on pseudo-differential operator algebras demonstrate integrability of Euler equations.
- Results connect algebraic supertrace structures to dynamical system integrability.

## Abstract

We describe supertraces on ``queerifications'' (see arxiv:2203.06917) of the algebras of matrices of ``complex size'', algebras of observables of Calogero-Moser model, Vasiliev higher spin algebras, and (super)algebras of pseudo-differential operators. In the latter case, the supertraces establish complete integrability of the analogs of Euler equations to be written.