Truncated Quantum Drinfeld Hecke Algebras and Hochschild Cohomology

@article{Grimley2018TruncatedQD,
  title={Truncated Quantum Drinfeld Hecke Algebras and Hochschild Cohomology},
  author={Lauren Grimley and Christine Uhl},
  journal={Algebras and Representation Theory},
  year={2018},
  volume={22},
  pages={569-587}
}
We consider deformations of quantum exterior algebras extended by finite groups. Among these deformations are a class of algebras which we call truncated quantum Drinfeld Hecke algebras in view of their relation to classical Drinfeld Hecke algebras. We give the necessary and sufficient conditions for which these algebras occur, using Bergman’s Diamond Lemma. We compute the relevant Hochschild cohomology to make explicit the connection between Hochschild cohomology and truncated quantum Drinfeld… 
View on Springer
arxiv.org
1 Citations
Methods Citations
1

One Citation

Color Lie rings and PBW deformations of skew group algebras

References

SHOWING 1-10 OF 24 REFERENCES
Hochschild cohomology and quantum Drinfeld Hecke algebras
Quantum Drinfeld Hecke algebras are generalizations of Drinfeld Hecke algebras in which polynomial rings are replaced by quantum polynomial rings. We identify these algebras as deformations of skew…
Quantum Drinfeld Hecke Algebras
Abstract We consider finite groups acting on quantum (or skew) polynomial rings. Deformations of the semidirect product of the quantum polynomial ring with the acting group extend symplectic…
PBW deformations of quantum symmetric algebras and their group extensions
We examine PBW deformations of finite group extensions of quantum symmetric algebras, in particular the quantum Drinfeld orbifold algebras defined by the first author. We give a homological…
Drinfeld orbifold algebras
We define Drinfeld orbifold algebras as filtered algebras deforming the skew group algebra (semi-direct product) arising from the action of a finite group on a polynomial ring. They simultaneously…
Hochschild cohomology of group extensions of quantum symmetric algebras
Quantum symmetric algebras (or noncommutative polynomial rings) arise in many places in mathematics. In this article we find the multiplicative structure of their Hochschild cohomology when the…
Quantum Drinfeld Orbifold Algebras
Quantum Drinfeld orbifold algebras are the generalizations of Drinfeld orbifold algebras, which are obtained by replacing polynomial rings by quantum polynomial rings. In [6], the authors give…
Quantum Drinfeld Hecke Algebras
Quantum Drinfeld Hecke algebras extend both Lusztig's graded Hecke algebras and the symplectic reflection algebras of Etingof and Ginzburg to the quantum setting. A quantum (or skew) polynomial ring…
Hochschild cohomology and graded Hecke algebras
We develop and collect techniques for determining Hochschild cohomology of skew group algebras S(V)#G and apply our results to graded Hecke algebras. We discuss the explicit computation of certain…
Group actions on algebras and the graded Lie structure of Hochschild cohomology
Drinfeld orbifold algebras for symmetric groups
...
...