Comparison between two differential graded algebras in Noncommutative Geometry
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2017
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| _version_ | 1866908769046233088 |
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| author | Chakraborty, Partha Sarathi Guin, Satyajit |
| author_facet | Chakraborty, Partha Sarathi Guin, Satyajit |
| contents | Starting with a spectral triple one can associate two canonical differential graded algebras (dga) defined by Connes and Fröhlich et al. For the classical spectral triples associated with compact Riemannian spin manifolds both these dgas coincide with the de-Rham dga. Therefore, both are candidates for the noncommutative space of differential forms. Here we compare these two dgas and observe that in a very precise sense Connes' dga is more informative than that of Fröhlich et al. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1708_03092 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Comparison between two differential graded algebras in Noncommutative Geometry Chakraborty, Partha Sarathi Guin, Satyajit Operator Algebras Quantum Algebra Primary 58B34, Secondary 46L87, 16E45 Starting with a spectral triple one can associate two canonical differential graded algebras (dga) defined by Connes and Fröhlich et al. For the classical spectral triples associated with compact Riemannian spin manifolds both these dgas coincide with the de-Rham dga. Therefore, both are candidates for the noncommutative space of differential forms. Here we compare these two dgas and observe that in a very precise sense Connes' dga is more informative than that of Fröhlich et al. |
| title | Comparison between two differential graded algebras in Noncommutative Geometry |
| topic | Operator Algebras Quantum Algebra Primary 58B34, Secondary 46L87, 16E45 |
| url | https://arxiv.org/abs/1708.03092 |