Minimal models for monomial algebras

Abstract: We will explain how to obtain the minimal model of a monomial associative algebra A, as in [1]. This multiplicative resolution has for generators the Anick chains of A, and as a differential a combinatorial `cutting' operation that splits such chains into `smaller' ones. Along with the formalism of Anick chains, our results make use of the algebraic discrete Morse theory of Jöllenbeck--Welker and Sköldberg, and the general theory of A_infty-(co)algebras. We aim to also mention certain open questions and conjectures that emerged from [1] and related work [2] with Dotsenko and Gélinas, and how one could begin elucidating similar results for other algebraic structures, where it is known the behaviour of the minimal model is already pathological.

[1] Minimal models for monomial algebras, Homology, Homotopy and Applications Volume 23 (2021) no. 1, pp. 341 – 366. (arXiv:1804.01435)

[2] Finite generation for Hochschild cohomology of Gorenstein monomial algebras, preprint arXiv:1909.00487

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

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Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)

Series comments: Description: Research webinar series

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