Creating quantum projective spaces by deforming q-symmetric algebras

Abstract: I will explain how to construct new "quantum projective spaces", in the form of Koszul, Calabi–Yau algebras with the Hilbert series of a polynomial ring. To do so we deform the relations of toric ones — q-symmetric algebras — using a diagrammatic calculus. Such deformations are unobstructed under suitable nondegeneracy conditions, which also guarantee that the algebras are Kontsevich's canonical quantizations of corresponding quadratic Poisson structures. This produces the first broad class of quadratic Poisson structures for which his quantization can be computed and shown to converge, as he conjectured in 2001. On the other hand, we also give examples of purely noncommutative deformations, which cannot be obtained by quantizing Poisson structures. This is joint work with Mykola Matviichuk and Brent Pym.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Comments: https://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09

Meeting ID: 918 7552 8987 Password: LAGOON

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Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)

Series comments: Description: Research webinar series

The LAGOON webinar series was supported as part of the International Centre for Mathematical Sciences (ICMS) and the Isaac Newton Institute for Mathematical Sciences (INI) Online Mathematical Sciences Seminars and is now sponsored by the University of Cologne and the University of Pavia. Please register here to obtain the Zoom link and password for the meetings.

LAGOON will take place online every last Wednesday of the month from 14:00-15:00 (Time Zone Berlin, Rome, Paris).

Videos of the talks can be viewed here.

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