Geometric Models for Noncommutative Algebra
by Ana Cannas da Silva, Alan Weinstein
Publisher: University of California at Berkeley 1998
Number of pages: 194
Noncommutative geometry is the study of noncommutative algebras as if they were algebras of functions on spaces, like the commutative algebras associated to affine algebraic varieties, differentiable manifolds, topological spaces, and measure spaces. In this book, we discuss several types of geometric objects which are closely related to noncommutative algebras.
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by Alain Connes, Matilde Marcolli - American Mathematical Society
The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role.
by Igor Nikolaev - arXiv
The book covers basics of noncommutative geometry and its applications in topology, algebraic geometry and number theory. Intended for the graduate students and faculty with interests in noncommutative geometry; they can be read by non-experts.
by Alain Connes - Academic Press
The definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics. Ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics.
by Travis Schedler - arXiv
In these notes, we give an example-motivated review of the deformation theory of associative algebras in terms of the Hochschild cochain complex as well as quantization of Poisson structures, and Kontsevich's formality theorem in the smooth setting.