The Weyl realizations of Lie algebras, and left-right duality (CROSBI ID 232006)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Meljanac, Stjepan ; Krešić-Jurić, Saša ; Martinić, Tea
engleski
The Weyl realizations of Lie algebras, and left-right duality
We investigate dual realizations of non-commutative spaces of Lie algebra type in terms of formal power series in the Weyl algebra. To each realization of a Lie algebra g we associate a star-product on the symmetric algebra S(g) and an ordering on the enveloping algebra U(g). Dual realizations of g are defined in terms of left- right duality of the star-products on S(g). It is shown that the dual realizations are related to an extension problem for g by shift operators whose action on U(g) describes left and right shift of the generators of U(g) in a given monomial. Using properties of the extended algebra, in the Weyl symmetric ordering we derive closed form expressions for the dual realizations of g in terms of two generating functions for the Bernoulli numbers. The theory is illustrated by considering the kappa- deformed space.
realizations of Lie algebras ; Weyl algebra ; star-product ; Weyl symmetric ordering ; left-right duality ; kappa-deformed space
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Podaci o izdanju
57 (5)
2016.
051704-1-051704-14
objavljeno
0022-2488
10.1063/1.4948991