Abstract
Let A≡KΔ /I be a factor of a path algebra. We develop a strategy to compute dim H1(A), the dimension of the first Hochschild cohomology group of A, using combinatorial data from (Δ,I). That allows us to connect dim H1(A) with the rank and p-rank of the fundamental group π1(Δ,I) of (Δ,I). We get explicit formulae for dim H1(A), when every path in Δ parallel to an arrow belongs to I or when I is homogeneous.
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