Abstract
Based on the minimal projective bimodule resolution, the Gerstenhaber bracket products on the Hochschild cohomology spaces for truncated quiver algebras are described explicitly in terms of parallel paths. As a consequence, for truncated basic cycle algebra Λ, each element in HH2(Λ) defines a noncommutative Poisson structure on Λ, and in turn defines the first multiplication of a one-parameter deformation of Λ.
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