Related papers: On rings and categories of general representations

Orbits of automorphism groups of partially ordered sets are not necessarily congruence classes, i.e. images of an order homomorphism. Based on so-called orbit categories a framework of factorisations and unfoldings is developed that…

We construct an abelian category C and exact functors in C which on the Grothendieck group descend to the action of a simply-laced quantum group in its adjoint representation. The braid group action in the adjoint representation lifts to an…

This paper is intended as a reference for some basic theory for dg categories and their bar complexes. Our modest goal is to carefully record the most important envelope operations can one perform on dg categories (in which one adjoins…

In this note, we define the Burnside ring of a monoid, generalizing the construction for groups. After giving foundational definitions, we characterize transitive M-sets and their automorphisms, then prove a structure theorem for a broad…

We give the classification of thick representations and dense representations of the symmetric group over a field of characteristic zero.

We give a representation of the classical theory of multiplicative arithmetic functions (MF)in the ring of symmetric polynomials. The basis of the ring of symmetric polynomials that we use is the isobaric basis, a basis especially sensitive…

A fundamental problem from invariant theory is to describe the endomorphism algebra of multilinear functions on a representation V invariant under the action of a group G. According to Weyl's classic, a first main (later: fundamental)…

We investigate the relationship between symmetric functions and the representation theory of operads, relative operads, and props. We extend the classical character map for symmetric sequences to relative bisymmetric sequences and symmetric…

The purpose of this book is to lay out certain aspects of descriptive set theory. After initially establishing notation and generalities we proceed to the following topics: partitions, semirings, rings, $\sigma$-rings, $\delta$-rings,…

We use the theory of regular objects in tensor categories to clarify the passage between braided multiplicative unitaries and multiplicative unitaries with projection. The braided multiplicative unitary and its semidirect product…

An extension of order theory is presented that serves as a formalism for the study of dendroidal sets analogously to way the formalism of order theory is used in the study of simplicial sets.

We present a general construction of the derived category of an algebra over an operad and establish its invariance properties. A central role is played by the enveloping operad of an algebra over an operad.

We introduce a nonsymmetric, associative tensor product among representations of Cuntz algebras by using embeddings. We show the decomposition formulae of tensor products for permutative representations explicitly We apply decomposition…

We give a historical perspective on the role of the cyclic category in the development of cyclic theory. This involves a continuous interplay between the extension in characteristic one and in S-algebras, of the traditional development of…

We consider a category whose morphisms are bordisms of $n$-dimensional pseudomanifolds equipped with a certain additional structure (coloring). On the other hand, we consider the product $G$ of $(n+1)$ copies of infinite symmetric group. We…

The construction of a quantum groupoid out of a double groupoid satisfying a filling condition and a perturbation datum is given. This extends previous work that appeared in math.QA/0308228. Several important classes of examples of tensor…

We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context.…

A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This…

With the development of topological field theory, the mathematical tool of the tensor category was also introduced into physics. Traditional group theory corresponds to a special category,group category. Tensor categories can describe…

We construct and study a nested sequence of finite symmetric tensor categories ${\rm Vec}=\mathcal{C}_0\subset \mathcal{C}_1\subset\cdots\subset \mathcal{C}_n\subset\cdots$ over a field of characteristic $2$ such that $\mathcal{C}_{2n}$ are…