You are not logged in |
THE CLIFFORD-DIRAC QUANTIZATION OF THE DE RHAM COMPLEX
- Speaker(s)
- TOMASZ MASZCZYK
- Affiliation
- Uniwersytet Warszawski, Poland
- Language of the talk
- English
- Date
- Jan. 8, 2025, 5:15 p.m.
- Link
- https://uw-edu-pl.zoom.us/j/95105055663?pwd=TTIvVkxmMndhaHpqMFUrdm8xbzlHdz09
- Information about the event
- IMPAN 405 & ZOOM
- Title in Polish
- THE CLIFFORD-DIRAC QUANTIZATION OF THE DE RHAM COMPLEX
- Seminar
- North Atlantic Noncommutative Geometry Seminar
We show that the de Rham complex is a degeneration of a one parameter family of filtered Z/2Z-graded algebras with a degree one almost derivation that are generically isomorphic to the Clifford algebra equipped with a Dirac operator. It turns out that the relation between the Dirac operator and the Levi-Civita connection is Hochschild-homological in nature. Moreover, the Levi-Civita connection itself can be obtained as a symmetric analog of the jacobiator for a symmetric bracket on functions. In turn, this symmetric bracket canonically extends to a graded symmetric bracket on the de Rham complex that is compatible with the differential. This leads to an intriguing symmetric bracket on the de Rham cohomology which is trivial in several regular examples, but could be an interesting invariant of singularities.
