Diagonalizable derivations of finite-dimensional algebras II

Daniel R. Farkas, Edward L. Green and Eduardo N. Marcos

Vol. 196 (2000), No. 2, 341–352

DOI: 10.2140/pjm.2000.196.341

Abstract

When an algebra is graded by a group, any additive character of the group induces a diagonalizable derivation of the ring. This construction is studied in detail for the case of a path algebra modulo relations and its fundamental group. We describe an injection of the character group into the first cohomology group following Assem-de la Peña. Rather general conditions are determined, in this context, which guarantee that a diagonalizable derivation is induced from the fundamental group.

Milestones

Received: 5 January 1999

Published: 1 December 2000