THE FUNDAMENTAL-GROUPS OF A TRIANGULAR ALGEBRA

A finite dimensional algebra A (over an algebraically closed field) is called triangular if its ordinary quiver has no oriented cycles. To e ach presentation (Q,I) of A is attached a fundamental group pi(1)(Q,I) , and A is called simply connected if pi(1)(Q,I) is trivial for every presentation of A. In this paper, we provide tools for computations wi th the fundamental groups, as well as criteria for simple connectednes s. We find relations between the fundamental groups of A and the first Hochschild cohomology H-1(A,A).