Koszul calculus

ANDREA SOLOTAR

Oberwolfach

Congreso; Hochschild Cohomology in Algebra, Geometry, and Topology; 2016

Mathematisches Forschungsinstitut Oberwolfach

I will present a calculus which is well-adapted to quadratic algebras. This calculus is defined in Koszul cohomology (homology) by cup products (cap products). Koszul homology and cohomology are interpreted in terms of derived categories. If the algebra is not Koszul, Koszul (co)homology provides dierent information than Hochschild (co)homology. Koszul homology is related to de Rham cohomology. If the algebra is Koszul, Koszul cohomology is related to Calabi-Yau property. The calculus is made explicit on a non-Koszul example.