Related papers: Traces on ideals in pivotal categories

We discuss that there exist at least two different choices in the signs of the induced A-infinity structures in shifting the degree of objects in an A-infinity category. We show that both of these choices are naturalin the sense that they…

In this paper, we define an invariant, which we believe should be the substitute for total K-theory in the case when there is one distinguished ideal. Moreover, some diagrams relating the new groups to the ordinary K-groups with…

In enumerative combinatorics, it is often a goal to enumerate both labeled and unlabeled structures of a given type. The theory of combinatorial species is a novel toolset which provides a rigorous foundation for dealing with the…

Multivariate versions of the Kronecker theorem in the continuous multivariate setting has recently been published. These theorems characterize the symbols that give rise to finite rank multidimensional Hankel and Toeplitz type operators…

We consider trace ideals in Noetherian rings and focus our attention to one-dimensional analytically irreducible local rings. For such rings we classify those Gorenstein rings which admit only a finite number of trace ideals.

We strengthen and put in a broader perspective previous results of the first two authors on colliding permutations. The key to the present approach is a new non-asymptotic invariant for graphs.

We consider changes in properties of a subgraph of an infinite graph resulting from the addition of open edges of Bernoulli percolation on the infinite graph to the subgraph. We give the triplet of an infinite graph, one of its subgraphs,…

We consider the universality for the trace invariants of $c_1 N \times \cdots \times c_D N$ tensors with i.i.d. complex random elements. In the case $c_1 = \cdots = c_D$, Gurau derived the universality in the limit $N \to \infty$ by…

We investigate, using the notion of linear quotients, significative classes of connected graphs whose monomial edge ideals, not necessarily squarefree, have linear resolution, in order to compute standard algebraic invariants of the…

We establish tetrahedral symmetries of 6j-symbols for arbitrary fusion categories under minimal assumptions. As a convenient tool for our calculations we introduce the notion of a veined fusion category, which is generated by a finite set…

We answer in the affirmative two conjectures made by Klein and Williams. First, in a range of dimensions, the equivariant Reidemeister trace defines a complete obstruction to removing $n$-periodic points from a self-map $f$. Second, this…

Using a new definition of a prime ideal of a skew brace A, on set Spec A of prime ideals of A we endow a spectral topology (in the sense of Grothendieck). We characterize irreducible closed subsets of Spec A and prove every irreducible…

We consider a class of biased random walks on infinite graphs and present several general results on the spectral radius of biased random walk.

We establish the geometry behind the quantum $6j$-symbols under only the admissibility conditions as in the definition of the Turaev-Viro invariants of $3$-manifolds. As a classification, we show that the $6$-tuples in the quantum…

In the paper an explicit formula for an arbitrary $6j$-symbol for finite-dimensional irreducible representations of the algebra $\mathfrak{gl}_3$ is derived. A $6j$-symbol is written as a result of substitution of $\pm 1$ into a series of…

We give an alternate conception of string diagrams as labeled 1-dimensional oriented cobordisms, the operad of which we denote by Cob/O, where O is the set of string labels. The axioms of traced (symmetric monoidal) categories are fully…

Given a finite tensor category $\mathcal{C}$, we prove that a modified trace on the tensor ideal of projective objects can be obtained from a suitable trivialization of the Nakayama functor as right $\mathcal{C}$-module functor. Using a…

We derive transformation rules for test ideals and $F$-singularities under an arbitrary finite surjective morphism $\pi : Y \to X$ of normal varieties in prime characteristic $p > 0$. The main technique is to relate homomorphisms $F_{*}…

We make a few remarks concerning pointwise extensions in a bicategory which include the case of bicategories of enriched categories. We show that extensions, pointwise or not, can be replaced by extensions along very special fully faithful…

We study the semi-classical trace formula at a critical energy level for an $h$-pseudo-differential operator on $\mathbb{R}^{n}$ whose principal symbol has a totally degenerate critical point for that energy. This problem is studied for a…