Koszul calculus

ANDREA SOLOTAR

Mar del Plata

Congreso; Algebras and Representation Theory IV; 2016

CIMPA y UNiv. Nac. de Mar del Plata

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.