Homogeneous ideals in Wick $*$-algebras
HTML articles powered by AMS MathViewer
- by Daniil Proskurin PDF
- Proc. Amer. Math. Soc. 126 (1998), 3371-3376 Request permission
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
- P. E. T. Jorgensen, L. M. Schmitt, and R. F. Werner, Positive representations of general commutation relations allowing Wick ordering, J. Funct. Anal. 134 (1995), no. 1, 33–99. MR 1359923, DOI 10.1006/jfan.1995.1139
- Marek Bożejko and Roland Speicher, Completely positive maps on Coxeter groups, deformed commutation relations, and operator spaces, Math. Ann. 300 (1994), no. 1, 97–120. MR 1289833, DOI 10.1007/BF01450478
Additional Information
- Daniil Proskurin
- Email: prosk@imath.kiev.ua
- 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
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 3371-3376
- MSC (1991): Primary 81R50, 47A62, 46L05
- DOI: https://doi.org/10.1090/S0002-9939-98-04305-6
- MathSciNet review: 1443406