Quasi-Hereditary Extension Algebras |
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Authors: | István Ágoston Vlastimil Dlab Erzsébet Lukács |
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Institution: | (1) Department of Algebra and Number Theory, Eötvös University, H-1053 Budapest, Hungary;(2) School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, K1S 5B6, Canada;(3) Department of Algebra, Technical University of Budapest, P.O. Box 91, H-1521 Budapest, Hungary |
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Abstract: | The paper is a continuation of the authors' study of quasi-hereditary algebras whose Yoneda extension algebras (homological duals) are quasi-hereditary. The so-called standard Koszul quasi-hereditary algebras, presented in this paper, have the property that their extension algebras are always quasi-hereditary. In the natural setting of graded Koszul algebras, the converse also holds: if the extension algebra of a graded Koszul quasi-hereditary algebra is quasi-hereditary, then the algebra must be standard Koszul. This implies that the class of graded standard Koszul quasi-hereditary algebras is closed with respect to homological duality. Another immediate consequence is the fact that all algebras corresponding to the blocks of the category O are standard Koszul. |
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Keywords: | quasi-hereditary algebra Yoneda extension algebra Koszul algebra Bernstein– Gelfand– Gelfand category O |
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