Algebras and Representation Theory

, Volume 20, Issue 3, pp 675–694 | Cite as

Koszul Duality for Semidirect Products and Generalized Takiff Algebras

  • Jacob Greenstein
  • Volodymyr Mazorchuk


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.


Module algebras Semi-direct products Graded algebras Koszul duality 

Mathematics Subject Classification (2010)

16S37 16W50 17B10 17B70 


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© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California RiversideRiversideUSA
  2. 2.Department of MathematicsUppsala UniversityUppsalaSweden

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