相关论文: Traces on ideals in pivotal categories

We interpret realizations of a graph on the sphere up to rotations as elements of a moduli space of curves of genus zero. We focus on those graphs that admit an assignment of edge lengths on the sphere resulting in a flexible object. Our…

For each $i \geq 0$, we study the trace ideal of the $i$-th exterior power of the module of differentials. We show that these ideals characterize the polynomial rank of graded rings and the formal power series rank of complete local rings,…

To supplement the already known classification of traces on classical pseudodifferential operators, we present a classification of traces on the algebras of odd-class pseudodifferential operators of non-positive order acting on smooth…

We study extended zeta-function residues on principal ideals of compact operators and their connections with Dixmier traces. We establish a Lidskii-type formula for continuous singular traces on these ideals. Using this formula, we obtain a…

This paper studies a class of binomial ideals associated to graphs with finite vertex sets. They generalize the binomial edge ideals, and they arise in the study of conditional independence ideals. A Gr\"obner basis can be computed by…

In the mid-1990s, two groups of authors independently obtained classifications of vertex-transitive graphs whose order is a product of two distinct primes. In the intervening years it has become clear that there is additional information…

Let G a be subgroup of SL(2,C), the group of 2x2 matrices of determinant 1 with complex entries. Let h map onto h(G) be a homomorphism. We call h a trace preserving homomorphism if tr(h(g))=tr(g) for all g in G,where tr(g) is the trace of…

We present an order-theoretic approach to the study of countably infinite locally 2-arc-transitive bipartite graphs. Our approach is motivated by techniques developed by Warren and others during the study of cycle-free partial orders. We…

We say that an ideal I is homogeneous, if its restriction to any I-positive subset is isomorphic to I. The paper investigates basic properties of this notion -- we give examples of homogeneous ideals and present some applications to…

We define the fundamental quandle of a spatial graph and several invariants derived from it. In the category of graph tangles, we define an invariant based on the walks in the graph and cocycles from nonabelian quandle cohomology.

In the present paper we set up a connection between the indices of the Tits algebras of a simple linear algebraic group $G$ and the degree one parameters of its motivic $J$-invariant. Our main technical tool are the second Chern class map…

We present the first complete derivation of the well-known asymptotic expansion of the SU(2) 6j symbol using a coherent state approach, in particular we succeed in computing the determinant of the Hessian matrix. To do so, we smear the…

In this work, we consider an extension of graphical models to random graphs, trees, and other objects. To do this, many fundamental concepts for multivariate random variables (e.g., marginal variables, Gibbs distribution, Markov properties)…

We revise our "Physical Traces" paper in the light of the results in "A Categorical Semantics of Quantum Protocols". The key fact is that the notion of a strongly compact closed category allows abstract notions of adjoint, bipartite…

Let H be a finite-dimensional unimodular pivotal quasi-Hopf algebra over a field k, and let H-mod be the pivotal tensor category of finite-dimensional H-modules. We give a bijection between left (resp. right) modified traces on the tensor…

For a braided vector space $(V,\sigma)$ with braiding $\sigma$ of Hecke type, we introduce three associative algebra structures on the space $\oplus_{p=0}^{M}\mathrm{End}S_\sigma^p(V)$ of graded endomorphisms of the quantum symmetric…

We show that the category of graphs has the structure of a 2-category with homotopy as the 2-cells. We then develop an explicit description of homotopies for finite graphs, in terms of what we call `spider moves'. We then create a category…

In fields ranging from business to systems biology, directed graphs with edges labeled by signs are used to model systems in a simple way: the nodes represent entities of some sort, and an edge indicates that one entity directly affects…

Let G be a finite graph on [n] = {1,2,3,...,n}, X a 2 times n matrix of indeterminates over a field K, and S = K[X] a polynomial ring over K. In this paper, we study about ideals I_G of S generated by 2-minors [i,j] of X which correspond to…

The category-valued trace assigns to a bimodule category over a linear monoidal category a linear category. It generalizes Drinfeld centers of monoidal categories and the relative Deligne product of bimodule categories. In this article, we…