Noncommutative geometry and quiver algebras
The authors introduce a double version of noncommutative geometry based on double derivations. Noncommutative symplectic geometry was first studied by Kontsevich. In this work, the authors consider the basic example of noncommutative symplectic manifold: the cotangent bundle of a smooth associative algebra. Applying Hamiltoninan reduction to the cotangent bundle, they find an interesting class of associative algebras. As a byproduct, the authors give a complete description of the Gerstenhaber algebra structure on polyvector fields.
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