Homology, Homotopy and Applications
Volume 23 (2021)
Minimal models for monomial algebras
Pages: 341 – 366
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.
monomial algebra, minimal model, $A_\infty$-algebra, rewriting theory, higher structure
2010 Mathematics Subject Classification
16E05, 16E40, 16E45, 18G15
Copyright © 2020, Pedro Tamaroff. Permission to copy for private use granted.
Received 4 September 2020
Received revised 7 September 2020
Accepted 7 September 2020
Published 9 December 2020