Related papers: Super Tannakian hulls

Modular functors, i.e. consistent systems of projective representations of mapping class groups of surfaces, have been constructed for non-semisimple modular categories already decades ago. Concepts from homological algebra have not been…

Let $D$ be a large category which is cocomplete. We construct a model structure (in the sense of Quillen) on the category of small functors from $D$ to simplicial sets. As an application we construct homotopy localization functors on the…

We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ''conformal vertex algebra'' or even more generally,…

We establish a duality between flat affine group schemes and rigid tensor categories equipped with a neutral fiber functor (called Tannakian lattice), both defined over a Dedekind ring. We use this duality and the known Tannakian duality…

Pre-Tannakian categories are a natural class of tensor categories that can be viewed as generalizations of algebraic groups. We define a pre-Tannkian category to be discrete if it is generated by an \'etale commutative algebra; these…

We show that the hypercohomology of most character twists of perverse sheaves on a complex abelian variety vanishes in all non-zero degrees. As a consequence we obtain a vanishing theorem for constructible sheaves and a relative vanishing…

A unique feature of N=6 conformal supergravity in three dimensions is that the super Cotton tensor W^{IJKL} can equivalently be viewed, via the Hodge duality, as the field strength of an Abelian vector multiplet, W^{IJ}. Using this…

We study several structure aspects of functor categories from a small additive category to a module category, in particular the category F(A,K) of functors from finitely generated free modules over a commutative ring A to vector spaces over…

This article deals with computing the cohomology of Schur functors applied to tautological bundles on super Grassmannians. We show that in a range of cases, the cohomology is a free module over the cohomology of the structure sheaf and that…

Let k be a field of characteristic zero. Etingof and Kazhdan constructed a quantisation U_h(b) of any Lie bialgebra b over k, which depends on the choice of an associator Phi. They prove moreover that this quantisation is functorial in b.…

We take a novel lattice-theoretic approach to the $\tau$-cluster morphism category $\mathfrak{T}(A)$ of a finite-dimensional algebra $A$ and define the category via the lattice of torsion classes $\mathrm{tors } A$. Using the lattice…

Considering a (co)homology theory $\mathbb{T}$ on a base category $\mathcal{C}$ as a fragment of a first-order logical theory we here construct an abelian category $\mathcal{A}[\mathbb{T}]$ which is universal with respect to models of…

We study a quantum version of the Kazhdan-Lusztig functor. Namely, we prove that there exists a fully faithfull exact tensor functor from the category of finite dimensional representations of the quantum affine algebra Uq(sl(n)) (with…

This is a survey on spherical Hopf algebras. We give criteria to decide when a Hopf algebra is spherical and collect examples. We discuss tilting modules as a mean to obtain a fusion subcategory of the non-degenerate quotient of the…

Fractional supersymmetric quantum mechanics of order $\lambda$ is realized in terms of the generators of a generalized deformed oscillator algebra and a Z$_{\lambda}$-grading structure is imposed on the Fock space of the latter. This…

If H is a strongly regular hypergroup, we show that the set of regular relations on H and the set of subhypergroups containing $0_{H}$ are two lattices that are isomorphic to each other. In the next step, we introduce and study the…

This is a generalization of some results of Ma-Sauter from module categories over artin algebras to more general functor categories (and partly to exact categories). In particular, we generalize the definition of a faithfully balanced…

We construct universal monoidal categories of topological tensor supermodules over the Lie superalgebras $\mathfrak{gl}(V\oplus \Pi V)$ and $\mathfrak{osp}(V\oplus \Pi V)$ associated with a Tate space $V$. Here $V\oplus \Pi V$ is a…

Let $G$ be the automorphism group of an extension $F|k$ of algebraically closed fields of characteristic zero and of transcendence degree $n$, $1\le n\le\infty$. In this paper we (i) construct some maximal closed non-open subgroups $G_v$,…

A theorem due to Kazhdan and Ziegler implies that, by substituting linear forms for its variables, a homogeneous polynomial of sufficiently high strength specialises to any given polynomial of the same degree in a bounded number of…