Generalized cyclic cohomology associated with deformed commutators
HTML articles powered by AMS MathViewer
- by Daoxing Xia PDF
- Proc. Amer. Math. Soc. 124 (1996), 1743-1753 Request permission
Abstract:
The generalized cyclic cohomology is introduced which is associated with $q$-deformed commutators $xy-qyx$. Some formulas related to the trace of the product of $q$-deformed commutators are established. The Chern character of odd dimension associated with $q$-deformed commutators is studied.References
- Alain Connes, Noncommutative differential geometry, Inst. Hautes Études Sci. Publ. Math. 62 (1985), 257–360. MR 823176
- Joachim Cuntz, Cyclic cohomology and $K$-homology, Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990) Math. Soc. Japan, Tokyo, 1991, pp. 969–978. MR 1159282
- P. E. T. Jørgensen and R. F. Werner, Coherent states of the $q$-canonical commutation relators, preprint.
- Achim Kempf, Multiparameter $R$-matrices, sub-quantum-groups and generalized twisting method, Proceedings of the XXth International Conference on Differential Geometric Methods in Theoretical Physics, Vol. 1, 2 (New York, 1991) World Sci. Publ., River Edge, NJ, 1992, pp. 546–550. MR 1225142
- Jean-Louis Loday and Daniel Quillen, Cyclic homology and the Lie algebra homology of matrices, Comment. Math. Helv. 59 (1984), no. 4, 569–591. MR 780077, DOI 10.1007/BF02566367
- Daniel Quillen, Algebra cochains and cyclic cohomology, Inst. Hautes Études Sci. Publ. Math. 68 (1988), 139–174 (1989). MR 1001452
- W. Pusz and S. L. Woronowicz, Twisted second quantization, Rep. Math. Phys. 27 (1989), no. 2, 231–257. MR 1067498, DOI 10.1016/0034-4877(89)90006-2
- Daoxing Xia, Trace formula for almost Lie group of operators and cyclic one-cocycles, Integral Equations Operator Theory 9 (1986), no. 4, 570–587. MR 853629, DOI 10.1007/BF01204629
- Daoxing Xia, On the almost unperturbed Schrödinger pair of operators, Integral Equations Operator Theory 12 (1989), no. 2, 241–279. MR 986597, DOI 10.1007/BF01195116
- Daoxing Xia, Principal distributions for almost unperturbed Schrödinger pairs of operators, Proc. Amer. Math. Soc. 112 (1991), no. 3, 745–754. MR 1042275, DOI 10.1090/S0002-9939-1991-1042275-9
- Daoxing Xia, Trace formulas for almost commuting operators, cyclic cohomology and subnormal operators, Integral Equations Operator Theory 14 (1991), no. 2, 276–298. MR 1090705, DOI 10.1007/BF01199909
- Daoxing Xia, A note on the trace formulas for almost commuting operators, Proc. Amer. Math. Soc. 116 (1992), no. 1, 135–141. MR 1092931, DOI 10.1090/S0002-9939-1992-1092931-2
- Daoxing Xia, Trace formula for the perturbation of partial differential operator and cyclic cocycle on a generalized Heisenberg group, Contributions to operator theory and its applications, Oper. Theory Adv. Appl., vol. 62, Birkhäuser, Basel, 1993, pp. 209–231. MR 1275388
- Daoxing Xia, Complete unitary invariant for some subnormal operator, Integral Equations Operator Theory 15 (1992), no. 1, 154–166. MR 1134692, DOI 10.1007/BF01193771
- —, A complete unitary invariant for subnormal operator with multiply connected spectrum, preprint.
Additional Information
- Daoxing Xia
- Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
- Email: xiad@ctrvax.vanderbilt.edu
- Received by editor(s): July 11, 1994
- Received by editor(s) in revised form: November 11, 1994
- Additional Notes: This work is supported in part by NSF grant DMS-9400766. Part of this paper has been presented to the Functional Analysis Colloquium of UCB, Seminar of Operator Theory of SUNY, Buffalo and GPOTS, Lincoln, Nebraska, 1994.
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 1743-1753
- MSC (1991): Primary 47A55; Secondary 47G05
- DOI: https://doi.org/10.1090/S0002-9939-96-03204-2
- MathSciNet review: 1307572