Abstract:
Let A≡KΔ /I be a factor of a path algebra. We develop a strategy to compute dim H 1(A), the dimension of the first Hochschild cohomology group of A, using combinatorial data from (Δ,I). That allows us to connect dim H 1(A) with the rank and p-rank of the fundamental group π1(Δ,I) of (Δ,I). We get explicit formulae for dim H 1(A), when every path in Δ parallel to an arrow belongs to I or when I is homogeneous.
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Received: 12 April 1999 / Revised version: 9 October 2000
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de la Peña, J., Saorín, M. On the first Hochschild cohomology group of an algebra. manuscripta math. 104, 431–442 (2001). https://doi.org/10.1007/s002290170017
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DOI: https://doi.org/10.1007/s002290170017