On H^1 of finite dimensional algebras
Claude Cibils
A para\^itre dans Proceedings  "Homologie et  th\'eorie des repr\'esentations" 
Vaquer\'\ias, C\'ordoba, Argentina, 1998. Pr\'epublication 1999-03, 
Universit\'e de Montpellier 2, France 
 
We review results on the first Hochschild  
cohomology vector space of a finite dimensional algebra, 
in particular for path algebras modulo a  
``pre-generated'' ideal. In case of a monomial  
algebra which quiver has no oriented cycles, a  
dimension formula is provided. The general  
monomial case will be considered in a  paper in  
progress with M. Saorin.