Ideals and Formal Morita Equivalence of Algebras
| dc.creator | Bursztyn, Henrique | |
| dc.creator | Waldmann, Stefan | |
| dc.date | 2000-05-23 | |
| dc.date.accessioned | 2026-07-07T04:35:28Z | |
| dc.date.available | 2026-07-07T04:35:28Z | |
| dc.description | Motivated by deformation quantization, we introduced in an earlier work the notion of formal Morita equivalence in the category of $^*$-algebras over a ring $\ring C$ which is the quadratic extension by $\im$ of an ordered ring $\ring R$. The goal of the present paper is twofold. First, we clarify the relationship between formal Morita equivalence, Ara's notion of Morita $^*$-equivalence of rings with involution, and strong Morita equivalence of $C^*$-algebras. Second, in the general setting of $^*$-algebras over $\ring C$, we define `closed' $^*$-ideals as the ones occuring as kernels of $^*$-representations of these algebras on pre-Hilbert spaces. These ideals form a lattice which we show is invariant under formal Morita equivalence. This result, when applied to Pedersen ideals of $C^*$-algebras, recovers the so-called Rieffel correspondence theorem. The triviality of the minimal element in the lattice of closed ideals, called the `minimal ideal', is also a formal Morita invariant and this fact can be used to describe a large class of examples of $^*$-algebras over $\ring C$ with equivalent representation theory but which are not formally Morita equivalent. We finally compute the closed $^*$-ideals of some $^*$-algebras arising in differential geometry. | |
| dc.description | LaTeX2e, 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0005227 | |
| dc.identifier | http://arxiv.org/abs/math/0005227 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59262 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Mathematical Physics | |
| dc.subject | Differential Geometry | |
| dc.subject | Rings and Algebras | |
| dc.title | Ideals and Formal Morita Equivalence of Algebras | |
| dc.type | text |