The first Hochschild (co)homology when adding arrows to a bound quiver algebra

Claude Cibils (1) , Marcelo Lanzilotta (2) , Eduardo Marcos , Sibylle Schroll , Andrea Solotar (3)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 IMERL - Instituto de Matemática y Estadística Rafael Laguardia [Montevideo]
3 Departamento de Matemática [Buenos Aires]

We provide a formula for the change of the dimension of the first Hoch\-schild cohomology vector space of bound quiver algebras when adding new arrows. For this purpose we show that there exists a short exact sequence which relates the first cohomology vector spaces of the algebras to the first relative cohomology. Moreover, we show that the first Hochschild homologies are isomorphic when adding new arrows.

Domaines: K-théorie et homologie [math.KT]; Anneaux et algèbres [math.RA]

Claude Cibils, Marcelo Lanzilotta, Eduardo Marcos, Sibylle Schroll, Andrea Solotar. The first Hochschild (co)homology when adding arrows to a bound quiver algebra. 2019. ⟨hal-02093478⟩