Algebraic versions of T² and of P¹×P¹ and Hochschild cohomology

Abstract: We analyze the Hochschild cohomology of triangular algebras that capture some aspects of the geometry and topology of the torus and of P¹×P¹, as well as of the deformations of these algebras. In particular, this shows that the cup product in the Hochschild cohomology of a triangular algebra generally does not follow the intuition from monomial algebras. Our examples also demonstrate that the Hochschild cohomology of a deformation of an algebra may not undergo a reduction of dimension but still have a different cup product structure, and that the Hochschild cohomologies of the deformations of two derivatively equivalent algebras can exhibit remarkably different behaviors. This is a joint work with Vladimir Dotsenko.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Comments: The Zoom link is

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

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