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Название: Geometric Models for Noncommutative Algebras

Автор: Ana Cannas da Silva, Alan Weinstein

Аннотация: Noncommutative geometry is the study of noncommutative algebras as if they were algebras of functions on spaces, like the commutative algebras associated to ane algebraic varieties, di erentiable manifolds, topological spaces, and measure spaces. In this book, we discuss several types of geometric objects (in the usual sense of sets with structure) which are closely related to noncommutative algebras. Central to the discussion are symplectic and Poisson manifolds, which arise when noncommutative algebras are obtained by deforming commutative algebras. We also make a detailed study of groupoids, whose role in noncommutative geometry has been stressed by Connes, as well as of Lie algebroids, the in nitesimal approximations to di erentiable groupoids.

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