THE CLIFFORD-DIRAC QUANTIZATION OF THE DE RHAM COMPLEX

Prelegent(ci)

TOMASZ MASZCZYK

Afiliacja

Uniwersytet Warszawski, Poland

Język referatu

angielski

Termin

8 stycznia 2025 17:15

Link

https://uw-edu-pl.zoom.us/j/95105055663?pwd=TTIvVkxmMndhaHpqMFUrdm8xbzlHdz09

Informacje na temat wydarzenia

IMPAN 405 & ZOOM

Tytuł w języku polskim

THE CLIFFORD-DIRAC QUANTIZATION OF THE DE RHAM COMPLEX

Seminarium

North Atlantic Noncommutative Geometry Seminar

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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.

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