Lie subalgebras of the matrix quantum pseudo differential operators

CARINA BOYALLIAN; KARINA BATISTELLI

Buenos Aires

Congreso; XXI Coloquio Latinoamericano de Álgebra; 2016

We give a complete description of the anti-involutions that preserve the principal gradation of the algebra Sq,N of N ×N matrix quantum pseudo-differential operators and we describe the Lie subalgebras of its minus fixed points. We obtain, up to conjugation, two families of anti-involutions that show quite different results. Finally, we give a geometric realization of each of these anti-involutions and show their corresponding subalgebras are of classical type.