Abstract
This paper is a continuous work of δ-Koszul algebras, which were first introduced by Green and Marcos in 2005 (see Green and Marcos, Commun Algebra 33(6):1753–1764, 2005). Let \(\mathcal{K}^{\delta}(A)\) be the category of δ-Koszul modules. It is proved that \(\mathcal{K}^{\delta}(A)\) preserves kernels of epimorphisms if and only if the “minimal Horseshoe Lemma” (“MHL” for short) holds. Further, a special class of δ-Koszul algebras named periodic δ -algebras are introduced, which have close connection with Koszul algebras and provide answers to the questions raised by Green and Marcos (Commun Algebra 33(6):1753–1764, 2005). Finally, we construct new periodic δ-algebras from the given ones in terms of one-point extension and sum-extension.
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Lü, JF. Notes on δ-Koszul Algebras. Appl Categor Struct 20, 143–159 (2012). https://doi.org/10.1007/s10485-010-9224-1
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DOI: https://doi.org/10.1007/s10485-010-9224-1