2001/12/21 by Sophie Dourlens, Dourlens, Sophie
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT) #Rings and Algebras (math.RA) #math.AT #math.KT #math.RA
paper · pdf · doi:10.48550/arxiv.math/0112243
20 pages, french
arxiv created 2001/12/21 · arxiv updated 2009/11/30
In order to study the Hochschild cohomology of triangular algebras \mathcal T, we construct a spectral sequence, whose terms are parametrized by the length of the trajectories of the quiver associated with \mathcal T, and which converges to HH^*(\mathcal T). We explicit its components, and its differentials which are sums of cup products. In case n=3, we study some properties of the differential at level 2. Finally, we apply these results to the paths algebra of a quiver without oriented cycles, and link them with previous results on the incidence algebra of a simplicial complex, and more generally on the morphisms algebra of certain categories.