Abstract
Let kQ be the path algebra of a quiver Q without oriented cycles with n vertices. An indecomposable kQ-module without self-extensions is called exceptional. The braid group B n with n − 1 generators acts naturally on the set of complete exceptional sequences. Crawley-Boevey (Proceedings of ICRA VI, Carleton-Ottawa, 1992) and Ringel (Contemp. Math. 1994, 171, 339–352) have pointed out that this action is transitive. The number of complete exceptional sequences for kQ representation finite will be computed here and it is shown to be independent of the orientation of the arrows of the quiver Q. The factor group of the braid group which acts freely on the set of complete exceptional sequences can be regarded as a subgroup of the symmetric group S ϵ n , where ϵ n is the number of complete exceptional sequences of the algebra kQ. This group is known for certain special types of quivers. Some other interesting relations of the acting group will be given.
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