Abstract
We investigate the stability of the super-KMS property under deformations. We show that a family of continuous deformations of the super-derivation in the quantum algebra yields a continuous family of deformed super-KMS functionals. These functionals define a family of cohomologous, entire cocycles.
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References
Araki, H.: On KMS states of aC*-dynamical system. In: Proc. of the Second Japan-U.S. Seminar onC*-Algebras and Applications to Physics, Los Angelos 1977. Araki, H., Kadison, R. (eds.). Berlin, Heidelberg, New York: Springer 1978
Bratelli, O., Robinson, D.W.: Operator algebras and quantum statistical mechanics, Vol. II. Berlin, Heidelberg, New York: Springer 1981
Bratelli, O., Kishimoto, A., Robinson, D.W.: Stability properties and the KMS condition. Commun. Math. Phys.61, 209–238 (1978)
Connes, A.: Private communication
Connes, A.: Noncommutative differential geometry. Publ. Math. IHES62, 257–360 (1985)
Connes, A.: Entire cyclic cohomology of banach algebras and characters ofθ-summable Fredholm modules. K-Theory1, 519–548 (1988)
Ernst, K., Feng, P., Jaffe, A., Lesniewski, A.: QuantumK-theory. II. Homotopy invariance of the Chern character. J. Funct. Anal. (to appear)
Getzler, E., Szenes, A.: On the Chern character of theta-summable Fredholm modules. J. Funct. Anal. (to appear)
Haag, R., Kastler, D., Trych-Pohlmeyer, E.: Stability and equilibrium states. Commun. Math. Phys.38, 173–194 (1974)
Jaffe, A., Lesniewski, A.: A priori estimates forN=2 Wess-Zumino models on a cylinder. Commun. Math. Phys.114, 553–575 (1988)
Jaffe, A., Lesniewski, A., Osterwalder, K.: QuantumK-theory. I. The Chern character. Commun. Math. Phys.118, 1–14 (1988)
Jaffe, A., Lesniewski, A., Osterwalder, K.: On super-KMS functionals and entire cyclic cohomology.K-Theory (to appear)
Jaffe, A., Lesniewski, A., Weitsman, J.: Index of a family of Dirac operators on loop space. Commun. Math. Phys.112, 75–88 (1987)
Jaffe, A., Lesniewski, A., Weitsman, J.: The two-dimensional,N=2 Wess-Zumino model on a cylinder. Commun. Math. Phys.114, 147–165 (1988)
Kastler, D.: Cyclic cocycles from graded KMS functionals. Commun. Math. Phys.121, 345–350 (1989)
Pedersen, G.:C*-Algebras and their automorphism groups. New York: Academic Press 1979
Robinson, D.W.: Return to equilibrium. Commun. Math. Phys.31, 171–189 (1973)
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Communicated by A. Jaffe
Supported in part by the Department of Energy under Grant DE-FG02-88ER25065
Visiting from the Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland
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Jaffe, A., Lesniewski, A. & Wisniowski, M. Deformations of super-KMS functionals. Commun.Math. Phys. 121, 527–540 (1989). https://doi.org/10.1007/BF01218155
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DOI: https://doi.org/10.1007/BF01218155