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Quasi-hereditary algebras, exact Borel subalgebras, A∞-categories and boxes
Institute of Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany.
Institute of Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany.ORCID iD: 0000-0002-1216-4024
Mechanics and Mathematics Faculty, Kiev National University, 01033 Kiev, Ukraine.
2014 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 262, p. 546-592Article in journal (Refereed) Published
Abstract [en]

Highest weight categories arising in Lie theory are known to be associated with finite dimensional quasi-hereditary algebras such as Schur algebras or blocks of category O. An analogue of the PBW theorem will be shown to hold for quasi-hereditary algebras: Up to Morita equivalence each such algebra has an exact Borel subalgebra. The category F(\Delta) of modules with standard (Verma, Weyl, …) filtration, which is exact, but rarely abelian, will be shown to be equivalent to the category of representations of a directed box. This box is constructed as a quotient of a dg algebra associated with the A-infinity-structure on Ext(\Delta,\Delta). Its underlying algebra is an exact Borel subalgebra.

Place, publisher, year, edition, pages
2014. Vol. 262, p. 546-592
Keywords [en]
Highest weight category, Quasi-hereditary algebra, Exact Borel subalgebra, Modules with standard filtrations, A-infinity-category, Differential graded category, Box
National Category
Algebra and Logic
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-359714DOI: 10.1016/j.aim.2014.05.016ISI: 000349742000015OAI: oai:DiVA.org:uu-359714DiVA, id: diva2:1245356
Available from: 2018-09-05 Created: 2018-09-05 Last updated: 2018-09-05Bibliographically approved

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