Koszulity and Koszul modules of dual extension algebras

Abstract

Let Aand Bbe algebras, and let T be the dual extension algebra of A and B. We provide a different method to prove that Tis Koszul if and only if both A and B are Koszul. Furthermore, we prove that an algebra is Koszul if and only if one of its iterated dual extension algebras is Koszul, if and only if all its iterated dual extension algebras are Koszul. Finally, we give a necessary and sufficient condition for a dual extension algebra to have the property that all linearly presented modules are Koszul modules, which provides an effective way to construct algebras with such a property.

Keywords

Dual extension / linearly presented / Koszul algebra / Koszul module

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