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We present the Gerstenhaber algebra structure on the Hochschild cohomology ofKoszul algebras defined by quivers and relations using the idea of homotopyliftings. E.L. Green, G. Hartman, E.N. Marcos and O. Solberg provided acanonical way of constructing a minimal projective bimodule resolution of aKoszul quiver algebra. The resolution has a comultiplicative structure which weuse to define homotopy lifting maps. We first present a short example thatdemonstrates the theory. We then study the Gerstenhaber algebra structure onHochschild cohomology of a family of bound quiver algebras, some members ofwhich are counterexamples to the Snashall-Solberg finite generation conjecture.We give examples of homotopy lifting maps for degree $2$ and degree $1$cocycles and draw connections to derivation operators. As an application, wedescribe Hochschild 2-cocycles satisfying the Maurer-Cartan equation.

Bracket structure on Hochschild cohomology of Koszul quiver algebras using homotopy liftings