Related papers: Invertible braided tensor categories
Over a field of characteristic $p>0$, the higher Verlinde categories $\mathrm{Ver}_{p^n}$ are obtained by taking the abelian envelope of quotients of the category of tilting modules for the algebraic group $\mathrm{SL}_2$. These symmetric…
Zesting of braided fusion categories is a procedure that can be used to obtain new modular categories from a modular category with non-trivial invertible objects. In this paper, we classify and construct all possible braided zesting data…
A strict monoidal category referred to as affine Brauer category $\mathcal{AB}$ is introduced over a commutative ring $\kappa$ containing multiplicative identity $1$ and invertible element $2$. We prove that morphism spaces in…
A renormalizable rigid supersymmetry for the four dimensional antisymmetric tensor field model in a curved space-time background is constructed. A closed algebra between the BRS and the supersymmetry operators is only realizable if the…
We begin with a brief sketch of what is known and conjectured concerning braided monoidal 2-categories and their applications to 4d topological quantum field theories and 2-tangles (surfaces embedded in 4-dimensional space). Then we give…
Given a commutative noetherian ring $R$ and a finite acyclic quiver $Q$, we study the tensor triangulated category $\mathcal{D}(RQ)$ endowed with the vertexwise tensor product. We find a description of the internal hom functor and show that…
We prove the existence of various adelic-style models for rigidly small-generated tensor-triangulated categories whose Balmer spectrum is a one-dimensional Noetherian topological space. This special case of our general programme of giving…
We investigate the braid group representations arising from categories of representations of twisted quantum doubles of finite groups. For these categories, we show that the resulting braid group representations always factor through finite…
A theorem of Pfister asserts that every $12$-dimensional quadratic form with trivial discriminant and trivial Clifford invariant over a field of characteristic different from $2$ decomposes as a tensor product of a binary quadratic form and…
Quivers over a fixed base set form a monoidal category with tensor product given by pullback. The quantum Yang-Baxter equation, or more properly the braid equation, is investigated in this setting. A solution of the braid equation in this…
We give an alternative presentation of braided monoidal categories. Instead of the usual associativity and braiding we have just one constraint (the b-structure). In the unital case, the coherence conditions for a b-structure are shown to…
We determine the structure of the cyclotomic Hecke algebra corresponding to the complex reflection group $G_{25}$ also when it is not semisimple, as long as the generators are diagonalizable. In particular, we classify all simple…
We introduce the oriented Brauer-Clifford and degenerate affine oriented Brauer-Clifford supercategories. These are diagrammatically defined monoidal supercategories which provide combinatorial models for certain natural monoidal…
We classify invertible 2-dimensional framed and $r$-spin topological field theories by computing the homotopy groups and the $k$-invariant of the corresponding bordism categories. The zeroth homotopy group of a bordism category is the usual…
We consider the derived category of permutation modules for a finite group, in positive characteristic. We stratify this tensor triangulated category using Brauer quotients. We describe the spectrum of its compact objects, by reducing the…
Let $\mathcal{O}_c$ be the category of finite-length central-charge-$c$ modules for the Virasoro Lie algebra whose composition factors are irreducible quotients of reducible Verma modules. Recently, it has been shown that $\mathcal{O}_c$…
We compute the group of Morita auto-equivalences of the even parts of the $ADE$ subfactors, and Galois conjugates. To achieve this we study the braided auto-equivalences of the Drinfeld centres of these categories. We give planar algebra…
We construct a finite dimensional quiver algebra from the non-simply laced type $B$ Dynkin diagram, which we call the type $B$ zigzag algebra. This leads to a faithful categorical action of the type $B$ braid group $\mathcal{A}(B)$, acting…
We initiate the representation theory of the degenerate affine periplectic Brauer algebra on $n$ strands by constructing its finite-dimensional calibrated representations when $n=2$. We show that any such representation that is…
We show that every Coxeter group that is not virtually abelian and for which all labels in the corresponding Coxeter graph are powers of 2 or infinity can be mapped onto uncountably many infinite 2-groups which, in addition, may be chosen…