Grothendieck topology of $C^*$-algebras
| Autor: | Ivankov, Petr R. |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | For any topological space there is a sheaf cohomology. A Grothendieck topology is a generalization of the classical topology such that it also possesses a sheaf cohomology. On the other hand any noncommutative $C^*$-algebra is a generalization of a locally compact Hausdorff space. Here we define a Grothendieck topology arising from $C^*$-algebras which is a generalization of the topology of the spectra of commutative $C^*$-algebras. This construction yields a noncommutative generalization of the sheaf cohomology of topological spaces. The presented here theory gives a unified approach to the Gelfand duality and the duality between the commutative von Neumann algebras and measure locales. The generalization of the Dixmier-Douady theory concerning $C^*$-algebras of foliations is also discussed. Comment: There is a fatal mistake in this article |
| Databáze: | arXiv |
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