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


Meljanac, Stjepan; Krešić-Jurić, Saša; Martinić, Tea
The Weyl realizations of Lie algebras, and left-right duality // Journal of mathematical physics, 57 (2016), 5; 051704-1 doi:10.1063/1.4948991 (međunarodna recenzija, članak, znanstveni)


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



POVEZANOST RADA


Projekt / tema
HRZZ-IP-2014-09-9582 - prema kvantnoj gravitaciji: nekomutativna geometrija, teorija polja i kozmologija (Stjepan Meljanac, )

Ustanove
Institut "Ruđer Bošković", Zagreb,
Prirodoslovno-matematički fakultet, Split

Časopis indeksira:


  • Current Contents Connect (CCC)
  • Web of Science Core Collection (WoSCC)
    • Science Citation Index Expanded (SCI-EXP)
    • SCI-EXP, SSCI i/ili A&HCI
  • Scopus


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