Related papers: Derived equivalences between subrings

We study the first-order axiomatisability of finite semiring interpretations or, equivalently, the question whether elementary equivalence and isomorphism coincide for valuations of atomic facts over a finite universe into a commutative…

The aim of this paper is to propose a theory of derivations for quandles. Given a quandle $A$ admitting an action by a quandle $Q$, derivations from $Q$ to $A$ are introduced as twisted analogues of quandle homomorphisms. It is shown that…

The main result of this paper is the construction of a trace and a trace pairing for endomorphisms satisfying suitable conditions in a monoidal category. This construction is a common generalization of the trace for endomorphisms of…

We exhibit a categorical equivalence between the class of odd or even involutive FL$_e$-chains and a class of direct systems of abelian $o$-groups. Restricting this equivalence only to odd or only to even involutive FL$_e$-chains or to…

We start from any small strict monoidal braided Ab-category and extend it to a monoidal nonstrict braided Ab-category which contains braided bialgebras. The objects of the original category turn out to be modules for these bialgebras

We generalise the notion of separable equivalence, originally presented by Linckelmann (2011), to an equivalence relation on additive categories. We use this generalisation to show that from an initial equivalence between two algebras we…

Minimal Q-graded subalgebras of semisimple Lie algebras are introduced, and it is proved that their derived algebras are abelian. Almost inner derivations of minimal Q-graded subalgebras are investigated, they are all inner derivations.…

We study abelian-by-cyclic Moufang loops. We construct all split $3$-divisible abelian-by-cyclic Moufang loops from so-called Moufang permutations on abelian groups $(X,+)$, which are permutations that deviate from an automorphism of…

Morphic sequences form a natural class of infinite sequences, typically defined as the coding of a fixed point of a morphism. Different morphisms and codings may yield the same morphic sequence. This paper investigates how to prove that two…

This paper provides the final ingredient in the development of the deformation theory of pretriangulated dg-categories endowed with a nice t-structure, which was initiated by the authors and is modeled after the previously developed…

From every pair of adjoint functors it is possible to produce a (possibly trivial) equivalence of categories by restricting to the subcategories where the unit and counit are isomorphisms. If we do this for the adjunction between effect…

We study the derived categories of small categories over commutative noetherian rings. Our main result is a parametrization of the localizing subcategories in terms of the spectrum of the ring and the localizing subcategories over residue…

In an abelian category $\mathscr{A}$ with small ${\rm Ext}$ groups, we show that there exists a one-to-one correspondence between any two of the following: balanced pairs, subfunctors $\mathcal{F}$ of ${\rm Ext}^{1}_{\mathscr{A}}(-,-)$ such…

Exact categories are a natural generalisation of abelian categories and provide a fertile ground to develop relative homological algebra. In this paper, starting from a class of relative Gorenstein projective objects in an exact category…

Let A be an exact category, that is, an extension-closed full subcategory of an abelian category. Firstly, we give some necessary and sufficient conditions for A to have almost split sequences. Then, we study when an almost split sequence…

Let $\phi\colon A\rightarrow B$ be an algebra extension. We prove that if $\phi$ is split, the derived-discreteness of $A$ implies the derived-discreteness of $B$; if $\phi$ is separable and the right $A$-module $B$ is projective, the…

We introduce and study a construction of higher derived brackets generated by a (not necessarily inner) derivation of a Lie superalgebra. Higher derived brackets generated by an element of a Lie superalgebra were introduced in our earlier…

For any positive integer $n$, $n$-derived-simple derived discrete algebras are classified up to derived equivalence. Furthermore, the Jordan-H\"older theorems for all kinds of derived categories of derived discrete algebras are obtained.

A finite group is said to be weakly separable if every algebraic isomorphism between two $S$-rings over this group is induced by a combinatorial isomorphism. In the paper we prove that every abelian weakly separable group belongs to one of…

In this paper we associate an abelian category to a finite directed graph and prove the categories arising from two graphs are equivalent if the incidence matrices of the graphs are shift equivalent. The abelian category is the quotient of…