CANONICAL Q-DEFORMATIONS OF NONCOMPACT LIE (SUPER-)ALGEBRAS

We propose a procedure for q-deformations of the real forms G of complex Lie (super-)algebras associated with (generalized) Cartan matrices. Our procedure gives different q-deformations for the non-conjugate Cartan subalgebras of G. We give several illustrations, eg., q-deformed Lorentz and conformal (super-)algebras. The q-deformed conformal algebra contains as a subalgebra a q-deformed Poincare algebra and as Hopf subalgebras two conjugate 11-generator q-deformed Weyl algebras. The q-deformed Lorentz algebra is a Hopf subalgebra of both Weyl algebras.