Steffen Koenig
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View article: Triangular decompositions: Reedy algebras and quasi-hereditary algebras
Triangular decompositions: Reedy algebras and quasi-hereditary algebras Open
Finite-dimensional Reedy algebras form a ring-theoretic analogue of Reedy categories and were recently proved to be quasi-hereditary. We identify Reedy algebras with quasi-hereditary algebras admitting a triangular (or Poincaré-Birkhoff-Wi…
View article: Ladders of recollements of abelian categories
Ladders of recollements of abelian categories Open
Ladders of recollements of abelian categories are introduced, and used to address three general problems. Ladders of a certain height allow to construct recollements of triangulated categories, involving derived categories and singularity …
View article: Recollements of abelian categories and ideals in heredity chains—a recursive approach to quasi-hereditary algebras
Recollements of abelian categories and ideals in heredity chains—a recursive approach to quasi-hereditary algebras Open
Recollements of abelian categories are used as a basis of a homological and recursive approach to quasi-hereditary algebras. This yields a homological proof of Dlab and Ringel’s characterisation of idempotent ideals occurring in heredity c…
View article: Recollements of abelian categories and ideals in heredity chains - a recursive approach to quasi-hereditary algebras
Recollements of abelian categories and ideals in heredity chains - a recursive approach to quasi-hereditary algebras Open
Recollements of abelian categories are used as a basis of a homological and recursive approach to quasi-hereditary algebras. This yields a homological proof of Dlab and Ringel's characterisation of idempotent ideals occuring in heredity ch…
View article: Rigidity dimension - a homological dimension measuring resolutions of algebras by algebras of finite global dimension
Rigidity dimension - a homological dimension measuring resolutions of algebras by algebras of finite global dimension Open
A new homological dimension is introduced to measure the quality of resolutions of `singular' finite dimensional algebras (of infinite global dimension) by `regular' ones (of finite global dimension). Upper bounds are established in terms …
View article: Derived equivalences, restriction to self-injective subalgebras and invariance of homological dimensions
Derived equivalences, restriction to self-injective subalgebras and invariance of homological dimensions Open
Derived equivalences between finite dimensional algebras do, in general, not pass to centraliser (or other) subalgebras, nor do they preserve homological invariants of the algebras, such as global or dominant dimension. We show that, howev…
View article: Recollements and stratifying ideals
Recollements and stratifying ideals Open
Surjective homological epimorphisms with stratifying kernel can be used to construct recollements of derived module categories. These `stratifying' recollements are derived from recollements of module categories. Can every recollement be p…
View article: Ortho-symmetric modules, Gorenstein algebras and derived equivalences
Ortho-symmetric modules, Gorenstein algebras and derived equivalences Open
A new homological symmetry condition is exhibited that extends and unifies several recently defined and widely used concepts. Applications include general constructions of tilting modules and derived equivalences, and characterisations of …