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Chrysostomos Psaroudakis

Publications and source records attributed to Chrysostomos Psaroudakis.

24 records · Page 2Linked to original sources
arXiv2016

Ladders of recollements, categories of monomorphisms and singularity categories

In this paper we show that the (un)bounded derived categories$\colon$(i) of the monomorphism category, (ii) of the morphism category and (iii) of the double morphism category, admit a periodic infinite ladder of recollements. These results are based on a characterization that we provide for a recollement of (compactly generated) triangulated categories to admit a ladder of some height going either upwards or downwards. Moreover, we introduce and study the singularity category of the monomorphism category over an Artin algebra $Λ$ and show that there is a periodic infinite ladder that connects this triangulated category with the standard singularity category of $Λ$. We also provide sufficient conditions for the monomorphism categories of two algebras to be singularly equivalent. The last aim of this paper is to study monomorphisms where the domain has finite projective dimension. We show that the latter category is a Gorenstein subcategory of the monomorphism category when $Λ$ is a Gorenstein Artin algebra. Finally, we consider the category of coherent functors over the stable category of this Gorenstein subcategory, and show that it carries a structure of a Gorenstein abelian category.

math.RT↗
arXiv2016

Gorenstein homological aspects of monomorphism categories via Morita rings

For any ring R the category of monomorphisms is a full subcategory of the morphsim category over R, where the latter is equivalent to the module category of the triangular matrix ring with entries the ring R. In this work, we consider the monomorphism category as a full subcategory of the module category over the Morita ring with all entries the ring R and zero bimodule homomorphisms. This approach provides an interesting link between Morita rings and monomorphism categories. The aim of this paper is two-fold. First, we construct Gorenstein-projective modules over Morita rings with zero bimodule homomorphisms and we provide sufficient conditions for such rings to be Gorenstein Artin algebras. This is the first part of our work which is strongly connected with monomorphism categories. In the second part, we investigate monomorphisms where the domain has finite projective dimension. In particular, we show that the latter category is a Gorenstein subcategory of the monomorphism category over a Gorenstein algebra. Finally, we consider the category of coherent functors over the stable category of this Gorenstein subcategory and show that it carries a structure of a Gorenstein abelian category.

math.RT↗
arXiv2014

Gorenstein categories, singular equivalences and finite generation of cohomology rings in recollements

Given an artin algebra $Λ$ with an idempotent element $a$ we compare the algebras $Λ$ and $aΛa$ with respect to Gorensteinness, singularity categories and the finite generation condition Fg for the Hochschild cohomology. In particular, we identify assumptions on the idempotent element $a$ which ensure that $Λ$ is Gorenstein if and only if $aΛa$ is Gorenstein, that the singularity categories of $Λ$ and $aΛa$ are equivalent and that Fg holds for $Λ$ if and only if Fg holds for $aΛa$. We approach the problem by using recollements of abelian categories and we prove the results concerning Gorensteinness and singularity categories in this general setting. The results are applied to stable categories of Cohen-Macaulay modules and classes of triangular matrix algebras and quotients of path algebras.

math.RT↗
arXiv2013

On Artin algebras arising from Morita contexts

We study Morita rings $Λ_{(ϕ,ψ)}=\bigl({smallmatrix} A &_AN_B_BM_A & B {smallmatrix}\bigr)$ in the context of Artin algebras from various perspectives. First we study covariant finite, contravariant finite, and functorially finite subcategories of the module category of a Morita ring when the bimodule homomorphisms $ϕ$ and $ψ$ are zero. Further we give bounds for the global dimension of a Morita ring $Λ_{(0,0)}$, regarded as an Artin algebra, in terms of the global dimensions of $A$ and $B$ in the case when both $ϕ$ and $ψ$ are zero. We illustrate our bounds with some examples. Finally we investigate when a Morita ring is a Gorenstein Artin algebra and then we determine all the Gorenstein-projective modules over the Morita ring with $A=N=M=B=Λ$, where $Λ$ is an Artin algebra.

math.RT↗
arXiv2013

Recollements of Module Categories

We establish a correspondence between recollements of abelian categories up to equivalence and certain TTF-triples. For a module category we show, moreover, a correspondence with idempotent ideals, recovering a theorem of Jans. Furthermore, we show that a recollement whose terms are module categories is equivalent to one induced by an idempotent element, thus answering a question by Kuhn.

math.RT↗