Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Homogeneous ideals in Wick -algebras

Author(s): 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 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:

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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