Supertraces on queerified algebras

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.