Related papers: Quantization as a functor

We provide three functorial extensions of the equivalence between localic etale groupoids and their quantales. The main result is a biequivalence between the bicategory of localic etale groupoids, with bi-actions as 1-cells, and a…

We show that in $K$-theory-like categories many corner embeddings into a discrete algebra of compact operators are invertible, and consequently functors on splitexact algebraic $KK$-theory are faithful if and only if they are faithful on…

In this article we establish the foundations of the Morita homotopy theory of C*-categories. Concretely, we construct a cofibrantly generated simplicial symmetric monoidal Quillen model structure M_Mor on the category C*cat1 of small unital…

We consider a class of map, recently derived in the context of cluster mutation. In this paper we start with a brief review of the quiver context, but then move onto a discussion of a related Poisson bracket, along with the Poisson algebra…

We formalize the arithmetic topology, i.e. a relationship between knots and primes. Namely, using the notion of a cluster C*-algebra we construct a functor from the category of 3-dimensional manifolds M to a category of algebraic number…

Extending the methods from our previous work on quantum knots and quantum graphs, we describe a general procedure for quantizing a large class of mathematical structures which includes, for example, knots, graphs, groups, algebraic…

We give a dynamical characterization of categorical Morita equivalence between compact quantum groups. More precisely, by a Tannaka-Krein type duality, a unital C*-algebra endowed with commuting actions of two compact quantum groups…

We produce graded monoidal categorifications of the quantum boson algebras in any symmetrizable Kac-Moody type. Our categories are defined in terms of diagrammatic generators and relations and have a faithful 2-representation on…

In this paper we prove a few propositions concerning factorizations of morphisms in pro categories, the most important of which solves an open problem of Isaksen concerning the existence of certain types of functorial factorizations. On our…

In this paper we prove the existence of isomorphisms between certain non-commutative algebras that are interesting from representation theoretic perspective and arise as quantizations of certain Poisson algebras. We show that quantizations…

We define the notion of braided Coxeter category, which is informally a tensor category carrying compatible, commuting actions of a generalised braid group B_W and Artin's braid groups B_n on the tensor powers of its objects. The data which…

In this work we give a deformation theoretical approach to the problem of quantization. First the notion of a deformation of a noncommutative ringed space over a commutative locally ringed space is introduced within a language coming from…

Let $A$ be a star product on a symplectic manifold $(M,\omega_0)$, $\frac{1}{t}[\omega]$ its Fedosov class, where $\omega$ is a deformation of $\omega_0$. We prove that for a complex polarization of $\omega$ there exists a commutative…

A group, defined as set with associative multiplication and inverse, is a natural structure describing the symmetry of a space. The concept of group generalizes to group objects internal to other categories than sets. But there are yet more…

For a class of symplectic manifolds, we introduce a functional which assigns a real number to any pair of continuous functions on the manifold. This functional has a number of interesting properties. On the one hand, it is Lipschitz with…

We develop a localisation theory for certain categories, yielding a 3-arrow calculus: Every morphism in the localisation is represented by a diagram of length 3, and two such diagrams represent the same morphism if and only if they can be…

We construct a category of fibrant objects $\mathbb{C}\langle P\rangle$ in the sense of K. Brown from any indexed frame (a kind of indexed poset generalizing triposes) $P$, and show that its homotopy category is the Barr-exact category…

We construct a mixed Hodge structure on the topological K-theory of smooth Poisson varieties, depending weakly on a choice of compactification. We establish a package of tools for calculations with these structures, such as functoriality…

This dissertation is an exposition of Kontsevich's proof of the formality theorem and the classification of deformation quantisation on a Poisson manifold. We begin with an account of the physical background and introduce the Weyl-Moyal…

Let $\mathfrak q$ be a finite-dimensional Lie algebra, $\vartheta\in Aut(\mathfrak q)$ a finite order automorphism, and $\mathfrak q_0$ the subalgebra of fixed points of $\vartheta$. Using $\vartheta$ one can construct a pencil $\mathcal P$…