Noncommutative Riemannian Geometry of Kronecker Algebras

Abstract: Differential calculus in noncommutative geometry come in several different flavors, and one of the more concrete versions goes by the name of derivation based differential calculus. This calculus is built from a disinguished Lie algebra of derivations, and lead to the formulation of differential forms, cohomology and connections. A fundamental question in noncommutative Riemannian geometry is the existence and uniqueness of a torsion free and metric compatible connection; i.e a Levi-Civita connection. For the moment, there are no general results addressing this question in this context, and I will present a case study based on a simple quiver path algebra, and show how the existence of a Levi-Civita connection depend on the choice of a Lie algebra of derivations.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | slides | video )

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Noncommutative geometry in NYC

Series comments: Noncommutative Geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. Our seminar welcomes talks in Number Theory, Geometric Topology and Representation Theory linked to the context of Operator Algebras. All talks are kept at the entry-level accessible to the graduate students and non-experts in the field. To join us click meet.google.com/zjd-ehrs-wtx (5 min in advance) and igor DOT v DOT nikolaev AT gmail DOT com to subscribe/unsubscribe for the mailing list, to propose a talk or to suggest a speaker. Pending speaker's consent, we record and publish all talks at the hyperlink "video" on speaker's profile at the "Past talks" section. The slides can be posted by providing the organizers with a link in the format "myschool.edu/~myfolder/myslides.pdf". The duration of talks is 1 hour plus or minus 10 minutes.

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