| 1. |
- Albeverio, Sergio, et al.
(författare)
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On *-representations of a deformation of a Wick analogue of the CAR algebra
- 2005
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Ingår i: Reports on Mathematical Physics. - 0034-4877. ; 56:2, s. 175-196-196
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Tidskriftsartikel (refereegranskat)abstract
- The classification of irreducible *-representations of deformations of canonical anti-commutation relations is given. A description of the corresponding enveloping C*-algebra is presented in terms of continuous matrix-functions satisfying certain boundary conditions.
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| 2. |
- Kuzmin, Olexiy, 1995, et al.
(författare)
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On q-tensor products of Cuntz algebras
- 2022
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Ingår i: International Journal of Mathematics. - 0129-167X. ; 33:2
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Tidskriftsartikel (refereegranskat)abstract
- We consider the C∗-algebra Eqn, m, which is a q-twist of two Cuntz-Toeplitz algebras. For the case |q| < 1, we give an explicit formula which untwists the q-deformation showing that the isomorphism class of Eqn, mdoes not depend on q. For the case |q| = 1, we give an explicit description of all ideals in Eqn, m. In particular, we show that Eqn, mcontains a unique largest ideal Mq. We identify Eqn, m/Mq with the Rieffel deformation of On ⊗Om and use a K-theoretical argument to show that the isomorphism class does not depend on q. The latter result holds true in a more general setting of multiparameter deformations.
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| 3. |
- Ostrovskyi, Vasyl, et al.
(författare)
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On structure of homogenenous Wick ideals in Wick *-algebras with braided coefficients
- 2012
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Ingår i: Reviews in Mathematical Physics. - 1793-6659 .- 0129-055X. ; 24:4, s. Art. no.1250007-
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Forskningsöversikt (refereegranskat)abstract
- We study a Wick ideal structure of quadratic *-algebras allowing Wick ordering with braided operator of coefficients. A construction of nested sequence of homogeneous Wick ideals of growing degree is presented. Representations of a Wick analogue of the CCR algebra with two degrees of freedom, annihilating certain homogeneous Wick ideals are described.
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| 4. |
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| 5. |
- Proskurin, D., et al.
(författare)
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On well-behaved representations of λ-deformed CCR
- 2017
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Ingår i: Methods of Functional Analysis and Topology. - 1029-3531 .- 2415-7503. ; 23:2, s. 192-205
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Tidskriftsartikel (refereegranskat)abstract
- We study well-behaved *-representations of a ?-deformation of Wick analog of CCR algebra. Homogeneous Wick ideals of degrees two and three are described. Well-behaved irreducible *-representations of quotients by these ideals are classified up to unitary equivalence.
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| 6. |
- Proskurin, D., et al.
(författare)
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Shilov Boundary for "Holomorphic Functions" on a Quantum Matrix Ball
- 2015
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Ingår i: Algebras and Representation Theory. - : Springer Science and Business Media LLC. - 1386-923X .- 1572-9079. ; 18:4, s. 917-929
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Tidskriftsartikel (refereegranskat)abstract
- We describe the Shilov boundary ideal for a q-analog of the algebra of holomorphic functions on the unit ball in the space of 2 x 2 matrices.
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