Trivial extension of Koszul algebras

Abstract

Let Λ be a Koszul algebra, and let Mbe a graded Λ-bimodule. We prove that the trivial extension algebra of Λ by Mis also a Koszul algebra whenever Mis Koszul as a left Λ-module. Applications and examples are also provided.

Keywords

Koszul algebra / Koszul module / trivial extension

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Higher Education Press and Springer-Verlag GmbH Germany