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We study locally conformally balanced metrics on almost abelian Lie algebras, namely solvable Lie algebras admitting an abelian ideal of codimension one, providing characterizations in every dimension. Moreover, we classify six-dimensional…

Coclass theory has been a highly successful approach towards the investigation and classification of finite nilpotent groups. Here we suggest a similar approach for finite nilpotent semigroups. This differs from the group theory setting in…

We study maximal subalgebras of an arbitrary finite dimensional algebra over a field, and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case, and…

We classify the category of finite-dimensional real division composition algebras having a non-abelian Lie algebra of derivations. Our complete and explicit classification is largely achieved by introducing the concept of a…

We explain how to attach a coalgebra $\mathcal C$ over a field $k$ to a small $k$-linear category $\mathsf E$ satisfying suitable finiteness conditions. In this context, we study full-and-faithfulness of the contramodule forgetful functor,…

We study the behaviour of almost split sequences and \art quivers of an order under rejection of bijective modules. In particular, we establish relations of stable categories and almost split sequences for an order $A$ and the order $A'$…

We prove that cellular Noetherian algebras with finite global dimension are split quasi-hereditary over a regular commutative Noetherian ring with finite Krull dimension and their quasi-hereditary structure is unique, up to equivalence. In…

The topological interpretation of modal logics provides descriptive languages and proof systems for reasoning about points of topological spaces. Recent work has been devoted to model checking of spatial logics on discrete spatial…

Highest weight categories arising in Lie theory are known to be associated with finite dimensional quasi-hereditary algebras such as Schur algebras or blocks of category $\mathcal O$. An analogue of the PBW theorem will be shown to hold for…

Words are sequences of letters over a finite alphabet. We study two intimately related topics for this object: quasi-randomness and limit theory. With respect to the first topic we investigate the notion of uniform distribution of letters…

We prove collective versions of semi-duality theorems for sets of almost (limitedly, order) L-weakly compact operators.

In this note we give a different and direct short proof to a previous result of Nastasescu and Torrecillas in \cite{NT} stating that if the rational part of any right $C^*$ module $M$ is a direct sumand in $M$ then $C$ must be finite…

A countable, bounded degree graph is almost finite if it has a tiling with isomorphic copies of finitely many F\o lner sets, and we call it strongly almost finite, if the tiling can be randomized so that the probability that a vertex is on…

We investigate a slight weakening of the classical property of strong approximation, which we call almost strong approximation, for connected reductive algebraic groups over global fields with respect to special sets of valuations. While…

We introduce the notion of a cellular system in order to deal with quasi-hereditary algebras. We shall prove that a necessary and sufficient condition for an algebra to be quasi-hereditary is the existence of a full divisible cellular…

This article begins the study of irreducible maps involving finite-dimensional uniserial modules over finite-dimensional associative algebras. We work on the classification of irreducible maps between two uniserials over triangular…

Approximable algebras were defined by Chen in his proof of the Fujita theorem in the arithmetic context. These were shown to not be necessarily subalgebras of section rings of big line bundles in a previous prepreint of the author. Here, we…

We show that the category of partial comodules over a Hopf algebra $H$ is comonadic over ${\sf Vect}_k$ and provide an explicit construction of this comonad using topological vector spaces. The case when $H$ is finite dimensional is treated…

Let H be a finite-dimensional quasibialgebra. We show that H is a quasi-Hopf algebra if and only if the category of its finite-dimensional left modules is rigid if and only if a structure theorem for Hopf modules over H holds. We also show…

Ringel's right-strongly quasi-hereditary algebras are a distinguished class of quasi-hereditary algebras of Cline-Parshall-Scott. We give characterizations of these algebras in terms of heredity chains and right rejective subcategories. We…