Related papers: Rees products and lexicographic shellability
We give a notably simpler and shorter proof of H. B. Neumann's result which is stated, cursorly, like this. For any well-ordered subset, A, of a totally ordered semigroup, the set of products of any finite number of elements of A is itself…
In the first part of the paper, we establish an homotopical version of the snail lemma (which is a generalization of the classical snake lemma). In the second part, we introduce the category $\mathbf{Seq}(\mathcal A)$ of sequentiable…
We study algebras and varieties where every non-trivial congruence has some class being a non-trivial subuniverse of the algebra in question. Then we focus on algebras where this non-trivial class is a unique non-singleton class of the…
Lee homology (a variant of Khovanov homology) over $\mathbb{Q}$ possesses the "canonical generators" as its basis. The generators (Lee's classes) $[\alpha(D, o)]$ are constructed combinatorially from an oriented link diagram $D$, one for…
Let $H$ be a group and $E$ a set such that $H \subseteq E$. We shall describe and classify up to an isomorphism of groups that stabilizes $H$ the set of all group structures that can be defined on $E$ such that $H$ is a subgroup of $E$. A…
Recollements of triangulated categories may be seen as exact sequences of such categories. Iterated recollements of triangulated categories are analogues of geometric or topological stratifications and of composition series of algebraic…
We prove standard results of group cohomology -- namely, existence of a long exact sequence, classification of torsors via the first cohomology group, Shapiro's lemma, the Hochschild-Serre spectral sequence, a decomposition of the cochain…
We introduce the notion of the space of parallel strings with partially summable labels, which can be viewed as a geometrically constructed group completion of the space of particles with labels. We utilize this to construct a machinery…
We start an analysis of geometric properties of a structure relative to a reduct. In particular, we look at definability of groups and fields in this context. In the relatively one-based case, every definable group is isogenous to a…
We introduce a natural class of models of random chain complexes of real vector spaces that some classical ensembles of random matrices, the length $1$ case. We are interested here in the homological properties of these random complexes.…
This expository note outlines why it is sometimes useful to consider the bigraded type A link homology theories as associated with the Lie algebras gl(N) instead of sl(N).
Persistence has proved to be a valuable tool to analyze real world data robustly. Several approaches to persistence have been attempted over time, some topological in flavor, based on the vector space-valued homology functor, other…
In recent work, Stokes and Vermant considered graph-of-groups realisations of hypergraphs as a new description of rigidity-theoretic problems. In this paper, we show that the infinitesimal aspects of graph-of-groups realisations can be…
Hom-Lie algebras are generalizations of Lie algebras that arise naturally in the study of nonassociative algebraic structures. In this paper, the concepts of solvable and nilpotent Hom-Lie algebras studied further. In the theory of groups,…
We investigate the matched product of solutions associated with right and left shelves. First, we prove that the requirements to provide the matched product of solutions that come from shelves can be simplified. Then we give conditions for…
Steinberg's tensor product theorem shows that for semisimple algebraic groups the study of irreducible representations of higher Frobenius kernels reduces to the study of irreducible representations of the first Frobenius kernel. In the…
We prove results describing the structure of a Chow ring associated to a product of graphs, which arises from the Gross-Schoen desingularization of a product of regular proper semi-stable curves over discrete valuation rings. By the works…
The notion of homomorphism indistinguishability offers a combinatorial framework for characterizing equivalence relations of graphs, in particular equivalences in counting logics within finite model theory. That is, for certain graph…
We consider approximating data structures with collections of the items that they contain. For examples, lists, binary trees, tuples, etc, can be approximated by sets or multisets of the items within them. Such approximations can be used to…
In this thesis we are interested in studying algebraic properties of monomial algebras, that can be linked to combinatorial structures, such as graphs and clutters, and to optimization problems. A goal here is to establish bridges between…