# Quantum affine wreath algebras

@article{Rosso2019QuantumAW, title={Quantum affine wreath algebras}, author={Daniele Rosso and Alistair Savage}, journal={arXiv: Quantum Algebra}, year={2019} }

To each symmetric algebra we associate a family of algebras that we call quantum affine wreath algebras. These can be viewed both as symmetric algebra deformations of affine Hecke algebras of type $A$ and as quantum deformations of affine wreath algebras. We study the structure theory of these new algebras and their natural cyclotomic quotients.

## 6 Citations

String diagrams and categorification

- Mathematics
- 2018

These are lectures notes for a mini-course given at the conference Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras, and Categorification in June 2018. The goal is to…

Quantum Frobenius Heisenberg categorification

- Mathematics
- 2020

We associate a diagrammatic monoidal category $\mathcal{H}\textit{eis}_k(A;z,t)$, which we call the quantum Frobenius Heisenberg category, to a symmetric Frobenius superalgebra $A$, a central charge…

Frobenius Heisenberg categorification

- MathematicsAlgebraic Combinatorics
- 2019

We associate a graded monoidal supercategory $\mathcal{H}\mathit{eis}_{F,\xi}$ to every graded Frobenius superalgebra $F$ and integer $\xi$. These categories, which categorify a broad range of…

Foundations of Frobenius Heisenberg categories

- MathematicsJournal of Algebra
- 2021

We describe bases for the morphism spaces of the Frobenius Heisenberg categories associated to a symmetric graded Frobenius algebra, proving several open conjectures. Our proof uses a categorical…

Affinization of monoidal categories

- MathematicsJournal de l’École polytechnique — Mathématiques
- 2020

We define the affinization of an arbitrary monoidal category $\mathcal{C}$, corresponding to the category of $\mathcal{C}$-diagrams on the cylinder. We also give an alternative characterization in…

Frobenius nil-Hecke algebras

- Mathematics
- 2020

To any Frobenius superalgebra $A$ we associate towers of Frobenius nilCoxeter algebras and Frobenius nilHecke algebras. These act naturally, via Frobeinus divided difference operators, on Frobenius…

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