Related papers: Graded relations on crossed products
We classify Galois objects for the dual of a group algebra of a finite group over an arbitrary field.
We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.
We develop a theory of crossed products by "actions" of Hecke pairs $(G, \Gamma)$, motivated by applications in non-abelian $C^*$-duality. Our approach gives back the usual crossed product construction whenever $G / \Gamma$ is a group and…
We introduce and study the class of spherically ordered groups. The notions of spherically ordered groups and their spectra of spherical orderability are introduced. Values of these spectra are found for a series of natural groups.
Full C*-crossed products by actions of locally compact groups are characterized via the existence of suitable maximal coactions, in analogy with Landstad's characterization of reduced crossed products.
We describe gradings by finite abelian groups on the associative algebras of infinite matrices with finitely many nonzero entries, over an algebraically closed field of characteristic zero.
We introduce the concept of an extension of a semilattice of groups $A$ by a group $G$ and describe all the extensions of this type which are equivalent to the crossed products $A*_\Theta G$ by twisted partial actions $\Theta$ of $G$ on…
We define graph products of families of pairs of groups and study the question when two such graph products are commensurable. As an application we prove linearity of certain graph products.
We study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. We develop an abstract theory that allows for generalizations of many of the fundamental results from the selfadjoint…
A graded-division algebra is an algebra graded by a group such that all nonzero homogeneous elements are invertible. This includes division algebras equipped with an arbitrary group grading (including the trivial grading). We show that a…
We define a general notion of centrally $\Gamma$-graded sets and groups and of their graded products, and prove some basic results about the corresponding categories: most importantly, they form braided monoidal categories. Here, $\Gamma$…
Morita equivalence of twisted inverse semigroup actions and discrete twisted partial actions are introduced. Morita equivalent actions have Morita equivalent crossed products.
We review the concept of a graded bundle as a natural generalisation of a vector bundle. Such geometries are particularly nice examples of more general graded manifolds. With hindsight there are many examples of graded bundles that appear…
We characterize supramenable groups in terms of existence of invariant probability measures for partial actions on compact Hausdorff spaces and existence of tracial states on partial crossed products. These characterizations show that, in…
We generalize the notion of identities among relations, well known for presentations of groups, to presentations of n-categories by polygraphs. To each polygraph, we associate a track n-category, generalizing the notion of crossed module…
This paper introduces product relation correlation, a measure of product relatedness that assesses the extent to which products may function as substitutes or complements through analysis of shared purchasing patterns. Product relation…
We study some classes of algebras of operators on non-Archimedean Banach spaces. In particular, we propose a non-Archimedean version of the crossed product construction.
We study linkedness of Cartesian product of graphs and prove that the product of an $a$-linked and a $b$-linked graphs is $(a+b-1)$-linked if the graphs are sufficiently large. Further bounds in terms of connectivity are shown. We determine…
We further the techniques developed by Etingof, Nikshych, and Ostrik in order to classify the $\mathcal{C}$-based equivalences between two $G$-graded extensions of $\mathcal{C}$. The main result of this paper (which follows from this…
Categories over a field $k$ can be graded by different groups in a connected way; we consider morphisms between these gradings in order to define the fundamental grading group. We prove that this group is isomorphic to the fundamental group…