Related papers: On Morita equivalences with endopermutation source…

To a bicomplex one can associate two natural filtrations, the column and row filtrations, and then two associated spectral sequences. This can be generalized to $N$-multicomplexes. We present a family of model category structures on the…

Inverse semigroups are the abstract counterparts of pseudogroups of transformations. The abstract counterparts of atlases in differential geometry are what Wagner termed `generalized heaps'. These are sets equipped with a ternary operation…

Since 2005 a new powerful invariant of an algebra emerged using earlier work of Horv\'ath, H\'ethelyi, K\"ulshammer and Murray. The authors studied Morita invariance of a sequence of ideals of the centre of a finite dimensional algebra over…

We prove that two dual operator algebras are weak$^*$ Morita equivalent if and only if they have equivalent categories of dual operator modules via completely contractive functors which are also weak$^*$-continuous on appropriate morphism…

This paper studies self-injective algebras of polynomial growth. We prove that the derived equivalence classification of weakly symmetric algebras of domestic type coincides with the classification up to stable equivalences (of Morita…

Stable equivalences of Morita type preserve many interesting properties and is proved to be the appropriate concept to study for equivalences between stable categories. Recently the singularity category attained much attraction and Xiao-Wu…

We show that Kessar's isotypy between Galois conjugate blocks of finite group algebras does not always lift to a $p$-permutation equivalence. We also provide examples of Galois conjugate blocks which are isotypic but not $p$-permutation…

We characterize the inverse semigroups that are Morita equivalent to graph inverse semigroups. We also consider a generalization to inverse semigroups associated with left cancellative categories.

In the first part of this article we prove that one of the conditions required in the original definition of nearly Frobenius algebra, the coassociativity, is redundant. Also, we determine the Frobenius dimension of the product and tensor…

Let $A$ be a finite-dimensional algebra over a field of characteristic $p>0$. We use a functorial approach involving torsion pairs to construct embeddings of endomorphism algebras of basic projective $A$--modules $P$ into those of the…

A general notion of a quasi-finite algebra is introduced as an algebra graded by the set of all integers equipped with topologies on the homogeneous subspaces satisfying certain properties. An analogue of the regular bimodule is introduced…

We consider the Lie algebra $\mathfrak{g}$ of a simple, simply connected algebraic group over a field of large positive characteristic. For each nilpotent orbit $\mathcal{O} \subseteq \mathfrak{g}$ we choose a representative $e\in…

The present article is concerned with division algebras that are structurally close to alternative algebras, in the sense that they satisfy some identity or other algebraic property that holds for all alternative division algebras.…

We obtain necessary and sufficient conditions to determine the existence of presymplectic forms of a given rank on all almost abelian Lie algebras. We also study the moduli space of presymplectic forms (this is the set of all closed 2-forms…

In this paper we investigate equivariant Morita theory for algebras with momentum maps and compute the equivariant Picard groupoid in terms of the Picard groupoid explicitly. We consider three types of Morita theory: ring-theoretic…

We define an equivalence relation called A-isotopy between finitely determined map-germs, which is a strengthened version of A-equivalence. We consider the number of A-isotopy classes of equidimensional Morin singularities, and some other…

Let N_1 (resp.N_2) be a nest A (resp. B) be the corresponding nest algebra, A_0 (resp. B_0) be the subalgebra of compact operators. We prove that the nests N_1, N_2 are isomorphic if and only if the algebras A, B are weakly-* Morita…

Given any quasi-countable, in particular any countable inverse semigroup $S$, we introduce a way to equip $S$ with a proper and right subinvariant extended metric. This generalizes the notion of proper, right invariant metrics for discrete…

Affine difference algebraic groups are a generalization of affine algebraic groups obtained by replacing algebraic equations with algebraic difference equations. We show that the isomorphism theorems from abstract group theory have…

The Graded Classification Conjecture states that for finite directed graphs $E$ and $F$, the associated Leavitt path algebras $L_\K(E)$ and $L_\K(F)$ are graded Morita equivalent, i.e., $\Gr L_\K(E) \approx_{\gr} \Gr L_\K(F)$, if and only…