Homological characterization of lean algebras |
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Authors: | István Ágoston Vlastimil Dlab Erzsébet Lukács |
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Affiliation: | (1) Mathematical Institute of the Hungarian Academy of Sciences, P.O. Box 127, 1364 Budapest, Hungary;(2) Department of Mathematics and Statistics, Carleton University, K1S 5B6 Ottawa, Ontario, Canada;(3) Department of Mathematics, Faculty of Transport Engineering, Technical University of Budapest, 1111 Budapest, Hungary |
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Abstract: | Certain classes of lean quasi-hereditary algebras play a central role in the representation theory of semisimple complex Lie algebras and algebraic groups. The concept of a lean semiprimary ring, introduced recently in [1] is given here a homological characterization in terms of the surjectivity of certain induced maps between Ext1-groups. A stronger condition requiring the surjectivity of the induced maps between Ext k -groups for allk≥1, which appears in the recent work of Cline, Parshall and Scott on Kazhdan-Lusztig theory, is shown to hold for a large class of lean quasi-hereditary algebras. Research partially supported by NSERC of Canada and by Hungarian National Foundation for Scientific Research grant no. 1903 Research partially supported by NSERC of Canada |
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Keywords: | Primary 16E99, 16S99 Secondary 17B10 |
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