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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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.


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Additional Information

Daniil Proskurin
Email: prosk@imath.kiev.ua

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04305-6
PII: S 0002-9939(98)04305-6
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