Foundations of Frobenius Heisenberg categories

  title={Foundations of Frobenius Heisenberg categories},
  author={Jonathan Brundan and Alistair Savage and Ben Webster},
  journal={Journal of Algebra},

Affine Oriented Frobenius Brauer Categories and General Linear Lie Superalgebras

To any Frobenius superalgebra A we associate an oriented Frobenius Brauer category and an affine oriented Frobenius Brauer categeory. We define natural actions of these categories on categories of

Diagrammatics for real supergroups

We introduce two families of diagrammatic monoidal supercategories. The first family, depending on an associative superalgebra, generalizes the oriented Brauer category. The second, depending on an

One-dimensional topological theories with defects: the linear case

. The paper studies the Karoubi envelope of a one-dimensional topological theory with defects and inner endpoints, defined over a field. It turns out that the Karoubi envelope is determined by a

Affine wreath product algebras with trace maps of generic parity

Abstract The goal of this article is to study the structure and representation theory of affine wreath product algebras and its cyclotomic quotients These algebras appear naturally in Heisenberg

Affine oriented Frobenius Brauer categories

Abstract To any Frobenius superalgebra A we associate an oriented Frobenius Brauer category and an affine oriented Frobenius Brauer category. We define natural actions of these categories on

Super rewriting theory and nondegeneracy of odd categorified sl(2)

We develop the rewriting theory for monoidal supercategories and 2-supercategories. This extends the theory of higher-dimensional rewriting established for (linear) 2-categories to the super setting,

Group partition categories

To every group $G$ we associate a linear monoidal category $\mathcal{P}\mathit{ar}(G)$ that we call a group partition category. We give explicit bases for the morphism spaces and also an efficient

Affinization of monoidal categories

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

Heisenberg Categorification and Wreath Deligne Category

We define a faithful linear monoidal functor from the partition category, and hence from Deligne’s category Rep(St), to the additive Karoubi envelope of the Heisenberg category. We show that the



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Heisenberg and Kac–Moody categorification

We show that any Abelian module category over the (degenerate or quantum) Heisenberg category satisfying suitable finiteness conditions may be viewed as a 2-representation over a corresponding

Monoidal Categories and Topological Field Theory

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Algebraic K-theory

A Category for the Adjoint Representation

Abstract We construct an abelian category C and exact functors in C which on the Grothendieck group descend to the action of a simply laced quantum group in its adjoint representation. The braid

Quantum Affine Wreath Algebras

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

Unfurling Khovanov-Lauda-Rouquier algebras

In this paper, we study the behavior of categorical actions of a Lie algebra $\mathfrak{g}$ under the deformation of their spectra. We give conditions under which the general point of a family of