Anick resolution and Koszul algebras of finite global dimension
Vladimir Dotsenko, Soutrik Roy Chowdhury
TL;DR
This paper uses the Anick resolution to analyze a specific associative algebra that challenges existing conjectures about Koszul algebras with finite global dimension.
Contribution
It demonstrates how to apply the Anick resolution to a newly identified algebra, providing insights into its structure and properties.
Findings
The algebra is a counterexample to Positselski's conjecture.
Application of Anick resolution reveals detailed algebraic structure.
The algebra has finite global dimension, contrary to previous assumptions.
Abstract
We show how to study a certain associative algebra recently discovered by Iyudu and Shkarin using the Anick resolution. This algebra is a counterexample to the conjecture of Positselski on Koszul algebras of finite global dimension.
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