Jordan type of Artinian algebras, finer invariants, and applications
Speaker:
Pedro Macias Marques, Universidade de Évora
Date and Time:
Monday, May 15, 2023 - 11:00am to 11:45am
Location:
Fields Institute, Room 230
Abstract:
We study Artinian algebras and consider the set of Jordan types of elements of the maximal ideal, i.e. the partition giving the Jordan blocks of the respective multiplication map. Jordan type has two main strengths. First, in the graded case, it is a finer invariant than the Lefschetz properties; second, Jordan type is well defined also on non-graded algebras, allowing us to generalize the definitions of week Lefschetz property and strong Lefschetz property to the non-graded case. In a joint work with Tony Iarrobino and Johanna Steinmeyer, we introduce new invariants built from Jordan type. They are finer invariants and have a nice behaviour with respect to deformation. We will give examples and propose several open problems.