Related papers: Tannakian formalism over fields with operators
We adapt a proof of Lascar in order to show the simplicity of the group of automorphisms fixing pointwise all non-generic elements for a class of uncountable models of suitable theories, encompassing both strongly minimal theories as well…
We present an analog to classic potential theory on weighted graphs. With nodes partitioned into exterior, boundary and interior nodes and an appropriate decomposition of the Laplacian, we define discrete analogues to the trace operators,…
Before we proposed an algebraic technics for the Hamiltonian approach to the evolution systems of partial differential equations, including systems with constraints. Here we further develop this approach and present the defining system of…
We present a definition of tensor fields which are average of tensors over a manifold, with a straightforward and natural definition of derivative for the averaged fields; which in turn makes a suitable and practical construction for the…
We study a class of tame $\mathcal{L}$-theories $T$ of topological fields and their $\mathcal{L}_\delta$-extension $T_{\delta}^*$ by a generic derivation $\delta$. The topological fields under consideration include henselian valued fields…
Operator systems are the unital self-adjoint subspaces of the bounded operators on a Hilbert space. Complex operator systems are an important category containing the C*-algebras and von Neumann algebras, which is increasingly of interest in…
This paper presents a new way of describing cross fields based on fourth order tensors. We prove that the new formulation is forming a linear space in $\mathbb{R}^9$. The algebraic structure of the tensors and their projections on…
We investigate composite models of gravity and explore how dynamical tensor fields can emerge within the functional renormalization group framework. We consider two prototype models: a fermionic theory and a scalar theory. In both cases, an…
We consider essentially small rigid tensor categories (not necessarily abelian) which have a faithful tensor functor to a category of super vector spaces over a field of characteristic 0. It is shown how to construct for each such tensor…
For any complex simple Lie algebra, we generalize primary fileds in the Wess-Zumino-Novikov-Witten conformal field theory with respect to the case of irregular singularities and we construct integral representations of hypergeometric…
We make a review on the recent progress in the operator algebraic approach to (super)conformal field theory. We discuss representation theory, classification results, full and boundary conformal field theories, relations to supervertex…
Motivated by team semantics and existential second-order logic, we develop a model-theoretic framework for studying second-order objects such as sets and relations. We introduce a notion of abstract elementary team categories that…
The study of topological quantum field theories increasingly relies upon concepts from higher-dimensional algebra such as n-categories and n-vector spaces. We review progress towards a definition of n-category suited for this purpose, and…
We shall discuss how the notions of multicategories and their linear representations are related with tensor categories. When one focuses on the ones arizing from planar diagrams, it particularly implies that there is a natural one-to-one…
We give a formalism of mixed sheaves on varieties over a subfield of the complex number field.
We develop a basic theory of affine group dg-schemes, their Lie algebraic counterparts and linear representations. We prove Tannaka type reconstruction theorems that an affine group dg-scheme can be recovered from the dg-tensor category of…
We describe a topological predual to differential forms constructed as an inductive limit of a sequence of Banach spaces. This subspace of currents has nice properties, in that Dirac chains and polyhedral chains are dense, and its operator…
Two variants of generalizations of Hankel operators to the case of linearly ordered abelian groups are considered, criteria of the boundedness and compactness of these operators are given, among them in terms of functions of bounded mean…
We prove a conjecture of Cautis and Sussan providing a categorification of the Boson-Fermion correspondence as formulated by Frenkel and Kac. We lift the Bernstein operators to infinite chain complexes in Khovanov's Heisenberg category H…
For each finite semisimple tensor category, we associate a quantum group (face algebra) whose comodule category is equivalent to the original one, in a simple natural manner. To do this, we also give a generalization of the Tannaka-Krein…