کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4668328 1345514 2007 63 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Noncommutative geometry and quiver algebras
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Noncommutative geometry and quiver algebras
چکیده انگلیسی

We develop a new framework for noncommutative differential geometry based on double derivations. This leads to the notion of moment map and of Hamiltonian reduction in noncommutative symplectic geometry. For any smooth associative algebra B, we define its noncommutative cotangent bundle T∗B, which is a basic example of noncommutative symplectic manifold. Applying Hamiltonian reduction to noncommutative cotangent bundles gives an interesting class of associative algebras, Π=Π(B), that includes preprojective algebras associated with quivers. Our formalism of noncommutative Hamiltonian reduction provides the space Π/[Π,Π] with a Lie algebra structure, analogous to the Poisson bracket on the zero fiber of the moment map. In the special case where Π is the preprojective algebra associated with a quiver of non-Dynkin type, we give a complete description of the Gerstenhaber algebra structure on the Hochschild cohomology of Π in terms of the Lie algebra Π/[Π,Π].

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 209, Issue 1, 15 February 2007, Pages 274-336