Presentation of Degree project E in Mathematics

  • Date: –17:30
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 Å64119, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala
  • Lecturer: Einar Waara (Uppsala)
  • Website
  • Organiser: Volodymyr Mazorchuk
  • Contact person: Volodymyr Mazorchuk
  • Seminarium

title: The weak Lefschetz property of Artinian monomial algebras

corresponding to simplicial complexes

abstarct:

 

Presentation of Master Thesis.

 

Given a graded Artinian algebra A one can investigate the (Weak/Strong) Lefschetz properties, that is, the conditions concerning the existence of a linear form L such that one can "move"

(in a full-rank fashion)

between the graded components of A via the multiplication maps given by L.

Given a simplicial complex one can describe it algebraically using its Stanley-Reisner ring. We consider a modified version of the Stanley-Reisner ring, an Artinian monomial algebra obtained by taking the quotient by all squares of variables, and see what it means to have the Weak Lefschetz property in terms of graph theoretic properties, in particular bipartiteness.