A family of *-algebras allowing Wick ordering: Fock representations and universal enveloping $C^*$-algebras

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dc.creatorJorgensen, Palle E. T.
dc.creatorProskurin, Daniil P.
dc.creatorSamoilenko, Yurii
dc.date2000-10-30
dc.date.accessioned2026-07-07T04:38:21Z
dc.date.available2026-07-07T04:38:21Z
dc.descriptionWe consider an abstract Wick ordering as a family of relations on elements a_i and define *-algebras by these relations. The relations are given by a fixed operator T:h\otimes h --> h \otimes h, where h is one-particle space, and they naturally define both a *-algebra and an inner-product space H_T, <.,.>_T. If a_i^* denotes the adjoint, i.e., <a_iϕ,ψ>_T=<ϕ,a_i^*ψ>_T, then we identify when <.,.>_T is positive semidefinite (the positivity question). In the case of deformations of the CCR-relations (the q_{ij}-CCR and the twisted CCR's), we work out the universal C*-algebras A, and we prove that, in these cases, the Fock representations of the A's are faithful.
dc.description9 pages, LaTeX2e document class "crckbked", NATO workshop proceedings (Kluwer) submission
dc.identifierhttps://arxiv.org/abs/math/0010308
dc.identifierhttp://arxiv.org/abs/math/0010308
dc.identifierNoncommutative Structures in Mathematics and Physics (Kiev, 2000) (S. Duplij and J. Wess, eds.), NATO Science Series II: Mathematics, Physics and Chemistry, vol. 22, Kluwer Academic Publishers, Dordrecht, 2001, pp. 321--329
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60246
dc.subjectQuantum Algebra
dc.subjectOperator Algebras
dc.subject46L55 (Primary), 81S05 (Secondary)
dc.titleA family of *-algebras allowing Wick ordering: Fock representations and universal enveloping $C^*$-algebras
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