Related papers: Free crossed resolutions for graph products of gro…
We partly generalize the estimate for the rank of intersection of subgroups in free products of groups, proved earlier by S.V.Ivanov and W.Dicks, to the case of free amalgamated products of groups with normal finite amalgamated subgroup. We…
This paper is concerned with the question of whether geometric structures such as cell complexes can be used to simultaneously describe the minimal free resolutions of all powers of a monomial ideal. We provide a full answer in the case of…
We introduce the notion of 3-crossed module, which extends the notions of 1-crossed module (Whitehead) and 2-crossed module (Conduch\'e). We show that the category of 3-crossed modules is equivalent to the category of simplicial groups…
In this paper, we introduced the concept of crossed module for Hom-Lie antialgebras. It is proved that the category of crossed modules for Hom-Lie antialgebras and the category of $Cat^1$-Hom-Lie antialgebras are equivalent to each other.…
The cocycle bicrossed product construction allows certain freedom in producing examples of locally compact quantum groups. We give an overview of some recent examples of this kind having remarkable properties.
In this paper, we define the pullback crossed modules in the category of racks which mainly based on a pullback diagram of rack morphisms with extra crossed module data on some of its arrows. Furthermore we prove that the conjugation…
This work creates two categories of "array-weighted sets" for the purposes of constructing universal matrix-normed spaces and algebras. These universal objects have the analogous universal property to the free vector space, lifting maps…
With a view to study problems of smoothability, we construct a minimal free resolution for the coordinate ring of an algebroid monomial curve associated to an $AS$ numerical semigroup (i.e. generated by an arithmetic sequence), obtained…
We consider the algebra M_k(C) of k-by-k matrices over the complex numbers and view it as a crossed product with a group G of order k by embedding G in the symmetric group S_k via the regular representation and embedding S_k in M_k(C) in…
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 investigate crossed products of Cuntz algebras by quasi-free actions of abelian groups. We prove that our algebras are AF-embeddable when actions satisfy a certain condition. We also give a necessary and sufficient condition that our…
Grouping the nodes of a graph into clusters is a standard technique for studying networks. We study a problem where we are given a directed network and are asked to partition the graph into a sequence of coherent groups. We assume that…
We determine all the multiplicity-free representations of the symmetric group. This project is motivated by a combinatorial problem involving systems of set-partitions with a specific pattern of intersection.
Results on the finiteness of induced crossed modules are proved both algebraically and topologically. Using the Van Kampen type theorem for the fundamental crossed module, applications are given to the 2-types of mapping cones of…
In this paper we define the notion of pullback lifting of a lifting crossed module over a crossed module morphism and interpret this notion in the category of group-groupoid actions as pullback action. Moreover, we give a criterion for the…
We present a geometrically oriented classification theory for non-Abelian extensions of groupoids generalizing the classification theory for Abelian extensions of groupoids by Westman as well as the familiar classification theory for…
We define group-twisted Alexander-Whitney and Eilenberg-Zilber maps for converting between bimodule resolutions of skew group algebras. These algebras are the natural semidirect products recording actions of finite groups by automorphisms.…
In one complex variable, the cross ratio is a well-known quantity associated with four given points in the complex plane that remains invariant under linear fractional maps. In particular, if one knows where three points in the complex…
We generalize graded Hecke algebras to include a twisting two-cocycle for the associated finite group. We give examples where the parameter spaces of the resulting twisted graded Hecke algebras are larger than that of the graded Hecke…
We consider a variety of connections between threshold graphs, shifted complexes, and simplicial complexes naturally formed from a graph. These graphical complexes include the independent set, neighborhood, and dominance complexes. We…