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Koszul Duality for Semidirect Products and Generalized Takiff Algebras
Univ Calif Riverside, Dept Math, Riverside, CA 92521 USA..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.ORCID iD: 0000-0002-4633-6218
2017 (English)In: Algebras and Representation Theory, ISSN 1386-923X, E-ISSN 1572-9079, Vol. 20, no 3, 675-694 p.Article in journal (Refereed) Published
Abstract [en]

We obtain Koszul-type dualities for categories of graded modules over a graded associative algebra which can be realized as the semidirect product of a bialgebra coinciding with its degree zero part and a graded module algebra for the latter. In particular, this applies to graded representations of the universal enveloping algebra of the Takiff Lie algebra (or the truncated current algebra) and its (super)analogues, and also to semidirect products of quantum groups with braided symmetric and exterior module algebras in case the latter are flat deformations of classical ones.

Place, publisher, year, edition, pages
2017. Vol. 20, no 3, 675-694 p.
Keyword [en]
Module algebras, Semi-direct products, Graded algebras, Koszul duality
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:uu:diva-323763DOI: 10.1007/s10468-016-9660-1ISI: 000401540300008OAI: oai:DiVA.org:uu-323763DiVA: diva2:1108325
Funder
Swedish Research CouncilKnut and Alice Wallenberg FoundationThe Royal Swedish Academy of Sciences
Available from: 2017-06-12 Created: 2017-06-12 Last updated: 2017-06-12Bibliographically approved

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