Gorenstein properly stratified algebras

Quasi-hereditary algebras are a class of finite-dimensional associative algebras that appear frequently in representation theory of associative algebras, but also of algebraic groups and semi-simple Lie algebras. They possess nice homological properties, like always having finite global dimension.  They have inspired several generalisations, such as standardly and properly stratified algebras, which retain several homological features and stratification properties.
Another important class of finite-dimensional algebras is given by Iwanaga–Gorenstein algebras, which unify algebras of finite global dimension and self-injective algebras within a common framework.

In this talk, we provide sufficient and necessary conditions for a standardly stratified algebra to be Iwanaga-Gorenstein and properly stratified making use of tilting theory and theory of recollements of triangulated categories. The first part is based on joint work with R. Marczinzik while the second part is based on ongoing work with S. Koenig and Y. Chen.

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There will be coffee and cake after the seminar in the common room.