Related papers: Characters and transfer maps via categorified trac…

We solve the problem of extension of characters of commutative subalgebras in associative (noncommutative) algebras for a class of subrings (Galois orders) in skew group rings. These results can be viewed as a noncommutative analogue of…

We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…

We describe integral lifts K(L), indexed by local fields L of degree n = [L:\Q_p], of the extraordinary cohomology theories K(n), and apply the generalized character theory of Hopkins, Kuhn and Ravenel to identify K(L)(BG) \otimes \Q$, for…

Let $G$ be a group acting on a field $L$, and suppose that $L /L^G$ is a finite extension. We show that the category of semilinear representations of $G$ over $L$ can be described in terms of the category of linear representations of $H$,…

The Gorenstein property in local algebra admits several characterizations via its module category. The goal of this paper is to collect and generalize such characterizations to the relative setting, i.e., to Gorenstein morphisms as defined…

We construct, in this paper, a generalization of the Dennis trace (for matrices) to the case of the supermatrices over an arbitrary (not necessarily commutative) superalgebra with unit. By analogy with the ungraded case, we show how it is…

We show that accounting for internal character among interacting, heterogeneous entities generates rich phase transition behavior between isolation and cohesive dynamical grouping. Our analytical and numerical calculations reveal different…

Let $\mathcal C$ be a small category with cofibrations. In this paper, we define the $K$-theory and Hochschild homology groups of $\mathcal C$ of order $Y$, where $Y$ is an ordered finite simplicial set with basepoint. Further, we construct…

In this paper we consider the problem of quantizing theories defined over configuration spaces described by non-commuting parameters. If one tries to do that by generalizing the path-integral formalism, the first problem one has to deal…

In this note we present a work in progress whose main purpose is to establish a categorified version of sheaf theory. We present a notion of derived categorical sheaves, which is a categorified version of the notion of complexes of sheaves…

We study a 2-functor that assigns to a bimodule category over a finite k-linear tensor category a k-linear abelian category. This 2-functor can be regarded as a category-valued trace for 1-morphisms in the tricategory of finite tensor…

A group-category is an additively semisimple category with a monoidal product structure in which the simple objects are invertible. For example in the category of representations of a group, 1-dimensional representations are the invertible…

For autonomous Tonelli systems on $\R^n$, we develop an intrinsic proof of the existence of generalized characteristics using sup-convolutions. This approach, together with convexity estimates for the fundamental solution, leads to new…

In this letter, we analyze the evolution of physical quantities due to the interaction of strings with background fields. We will obtain the characteristic function for such a string theoretical process. This will be done by generalizing…

Expanding products of invariant functions of a group element as a series in the basis of characters of the irreducible representations of a group is widely used in many areas of physics and related fields. In this contribution a formula to…

The Euler characteristic of a finite category is defined and shown to be compatible with Euler characteristics of other types of object, including orbifolds. A formula for the cardinality of the colimit of a diagram of sets is proved,…

Categorical compositional distributional semantics is a model of natural language; it combines the statistical vector space models of words with the compositional models of grammar. We formalise in this model the generalised quantifier…

Using the higher tame symbol and Kawada and Satake's Witt vector method, A. N. Parshin developed class field theory for higher local fields, defining reciprocity maps separately for the tamely ramified and wildly ramified cases. We extend…

A classical result of Littlewood gives a factorisation for the Schur function at a set of variables "twisted" by a primitive $t$-th root of unity, characterised by the core and quotient of the indexing partition. While somewhat neglected,…

Gcharacter tables of a finite group G were defined before. These tables can be very useful to obtain certain structural information of a normal subgroup from the character table of G. We analyze certain structural properties of normal…