Lie subalgebras of the matrix quantum pseudo differential operators

TL;DR

This paper classifies anti-involutions preserving the principal gradation in matrix quantum pseudodifferential operators and describes the associated Lie subalgebras of fixed points.

Contribution

It provides a complete characterization of anti-involutions and the structure of their fixed point Lie subalgebras in this algebraic setting.

Findings

Classification of anti-involutions preserving principal gradation

Description of Lie subalgebras of fixed points

Structural insights into matrix quantum pseudodifferential operators

Abstract

We give a complete description of the anti-involutions that preserve the principal gradation of the algebra of matrix quantum pseudodifferential operators and we describe the Lie subalgebras of its minus fixed points.