Algebraic Rieffel Induction, Formal Morita Equivalence, and Applications to Deformation Quantization
| dc.creator | Bursztyn, Henrique | |
| dc.creator | Waldmann, Stefan | |
| dc.date | 1999-12-22 | |
| dc.date | 2000-01-30 | |
| dc.date.accessioned | 2026-07-07T05:32:25Z | |
| dc.date.available | 2026-07-07T05:32:25Z | |
| dc.description | In this paper we consider algebras with involution over a ring C which is given by the quadratic extension by i of an ordered ring R. We discuss the *-representation theory of such *-algebras on pre-Hilbert spaces over C and develop the notions of Rieffel induction and formal Morita equivalence for this category analogously to the situation for C^*-algebras. Throughout this paper the notion of positive functionals and positive algebra elements will be crucial for all constructions. As in the case of C^*-algebras, we show that the GNS construction of *-representations can be understood as Rieffel induction and, moreover, that formal Morita equivalence of two *-algebras, which is defined by the existence of a bimodule with certain additional structures, implies the equivalence of the categories of strongly non-degenerate *-representations of the two *-algebras. We discuss various examples like finite rank operators on pre-Hilbert spaces and matrix algebras over *-algebras. Formal Morita equivalence is shown to imply Morita equivalence in the ring-theoretic framework. Finally we apply our considerations to deformation theory and in particular to deformation quantization and discuss the classical limit and the deformation of equivalence bimodules. | |
| dc.description | LaTeX2e, 51pages, minor typos corrected and Note/references added | |
| dc.identifier | https://arxiv.org/abs/math/9912182 | |
| dc.identifier | http://arxiv.org/abs/math/9912182 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79654 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Mathematical Physics | |
| dc.subject | Symplectic Geometry | |
| dc.title | Algebraic Rieffel Induction, Formal Morita Equivalence, and Applications to Deformation Quantization | |
| dc.type | text |