Naslov
The Weyl realizations of Lie algebras, and left-right duality

Autori
Meljanac, Stjepan ; Krešić-Jurić, Saša ; Martinić, Tea

Izvornik
Journal of mathematical physics (0022-2488) 57 (2016), 5; 051704-1

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
realizations of Lie algebras ; Weyl algebra ; star-product ; Weyl symmetric ordering ; left-right duality ; kappa-deformed space

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Fizika

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