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
Full-text PDF Free Access
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.
- 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 https://doi.org/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 https://doi.org/10.1007/BF01450478
- 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.
- M. Bożejko and R. Speicher. Completely positive maps on Coxeter groups, deformed commutation relations, and operator spaces. Mat. Ann. 300 (1994), 97–120.
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