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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Acknowledgments
We are grateful to Leonid Positselski for drawing our attention to the fact that the list of algebras in [Citation7] contains a counterexample to his conjecture. Ivan Yudin informed us that it is also possible to establish the claim on Koszulness by a careful examination of the two Anick resolutions for the orderings x>y>z and y>x>z for the original algebra; his argument utilizes Ufnarovski’s graph for generating Anick chains [Citation10, Citation9]; we are very thankful for that remark.