Geodesic
Minimal models for monomial algebras
Homology, homotopy, and applications, Tome 23 (2021) no. 1, pp. 341-366.

Voir la notice de l'article provenant de la source International Press of Boston

We give, for any monomial algebra $A$, an explicit description of its minimal model, which also provides us with formulas for a canonical $A_\infty$‑structure on the Ext-algebra of the trivial $A$‑module. We do this by exploiting the combinatorics of chains going back to works of Anick, Green, Happel and Zacharia, and the algebraic discrete Morse theory of Jöllenbeck, Welker and Sköldberg. We then show how this result can be used to obtain models for algebras with a chosen Gröbner basis, and briefly outline how to compute some classical homological invariants with it.
DOI : 10.4310/HHA.2021.v23.n1.a18
Classification : 16E05, 16E40, 16E45, 18G15
Keywords: monomial algebra, minimal model, $A_\infty$-algebra, rewriting theory, higher structure 
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Pedro Tamaroff. Minimal models for monomial algebras. Homology, homotopy, and applications, Tome 23 (2021) no. 1, pp. 341-366. doi : 10.4310/HHA.2021.v23.n1.a18. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2021.v23.n1.a18/

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