Generalization of Weyl realization to a class of Lie superalgebras

Abstract

This paper generalizes Weyl realization to a class of Lie superalgebras g = g 0 ⊕g 1 satisfying [g 1 , g 1 ] = {0}. First, we give a novel proof of the Weyl realization of a Lie algebra g 0 by deriving a functional equation for the function that defines the realization. We show that this equation has a unique solution given by the generating function for the Bernoulli numbers. This method is then generalized to Lie superalgebras of the above type. * meljanac@irb.hr † dpikutic@irb.hr ‡ skresic@pmfst.hr

Generalized Heisenberg algebra applied to realizations of the orthogonal, Lorentz and Poincare algebras and their dual extensions

“…Indeed, the first two relations in (26) follow trivially while the third relation is a direct consequence of Eq. ( 19).…”

Symmetric ordering and Weyl realizations for quantum Minkowski spaces

“…Weyl realizations 1 related to Lie algebras were studied in [26,57,58,59,60] and for superalgebras in [61]. In the present paper, we review Weyl realizations of Lie deformed spaces and corresponding star products, as well as the twist corresponding to Weyl realization and coproduct of momenta.…”

“…The Weyl realization for κ-deformed Euclidean space was found in [26] and the Weyl realization for the orthogonal, Lorentz and Poincaré algebras was investigated in [60]. Generalization of the Weyl realization to a class of Lie superalgebras was given in [61].…”