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Proceedings of the American Mathematical Society

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Homogeneous ideals in Wick $*$-algebras

Author: Daniil Proskurin
Journal: Proc. Amer. Math. Soc. 126 (1998), 3371-3376
MSC (1991): Primary 81R50, 47A62, 46L05
MathSciNet review: 1443406
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Abstract: The necessary and sufficient condition for the family of homogeneous elements to determine a Wick ideal is presented. The structure of homogeneous Wick ideals with degree higher than 2 is discussed. For the braided operator $T$ a formula to calculate the largest cubic ideal when the quadratic one is known is obtained. Irreducible $*$-representations of the $\mu$-CAR algebra are classified.

References [Enhancements On Off] (What's this?)

  • 1. P. E. T. Jørgensen, L. M. Schmitt and R. F. Werner. Positive representations of general commutation relations allowing Wick ordering. J. Funct. Anal. 134, no. 1 (1995), 33-99. MR 96h:81033
  • 2. M. Bo\.{z}ejko and R. Speicher. Completely positive maps on Coxeter groups, deformed commutation relations, and operator spaces. Mat. Ann. 300 (1994), 97-120. MR 95g:46105

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Additional Information

Daniil Proskurin

Received by editor(s): November 21, 1996
Received by editor(s) in revised form: December 10, 1996
Additional Notes: This work was partially supported by the CRDF, grant no. 292
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society