Minimal models for monomial algebras

Abstract

Using combinatorics of chains going back to works of Anick, Green, Happel and Zacharia, we give, for any monomial algebra $A$, an explicit description of its minimal model. This 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.

References in corpus (6)

• Sur les A-infini catégories
• Quillen homology for operads via Gröbner bases
• Transferring $A_{\infty }$ (strongly homotopy associative) structures
• Homotopy theory of homotopy algebras
• Finite generation for Hochschild cohomology of Gorenstein monomial algebras
• The A-infinity Centre of the Yoneda Algebra and the Characteristic Action of Hochschild Cohomology on the Derived Category

Cited by in corpus (6)

• Finite generation for Hochschild cohomology of Gorenstein monomial algebras
• Tangent complexes and the Diamond Lemma
• $A_{\infty }$-coderivations and the Gerstenhaber bracket on Hochschild cohomology
• On a theorem of B. Keller on Yoneda algebras of simple modules
• The $\mathrm{Ext}$-algebra of standard modules over dual extension algebras
• The Tamarkin--Tsygan calculus of an algebra a la Stasheff