Geometric Models for Noncommutative Algebras 2024 pdf epub mobi 電子書下載

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Geometric Models for Noncommutative Algebras pdf epub mobi 著者簡介

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The volume is based on a course, "Geometric Models for Noncommutative Algebras" taught by Professor Weinstein at Berkeley. Noncommutative geometry is the study of noncommutative algebras as if they were algebras of functions on spaces, for example, the commutative algebras associated to affine algebraic varieties, differentiable manifolds, topological spaces, and measure spaces. In this work, the authors discuss several types of geometric objects (in the usual sense of sets with structure) that 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. The authors also give a detailed study of groupoids (whose role in noncommutative geometry has been stressed by Connes) as well as of Lie algebroids, the infinitesimal approximations to differentiable groupoids.

Featured are many interesting examples, applications, and exercises. The book starts with basic definitions and builds to (still) open questions. It is suitable for use as a graduate text. An extensive bibliography and index are included.

Geometric Models for Noncommutative Algebras 2024 pdf epub mobi 電子書下載

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發表於2024-11-23

Geometric Models for Noncommutative Algebras 2024 pdf epub mobi 電子書下載

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Geometric Models for Noncommutative Algebras pdf epub mobi 讀後感

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群胚（groupoid）是非交換數學的一個基本研究對象，下麵我們先給齣其公理性定義，並用範疇語言做一個等價刻畫，再比較一下群胚與群的差彆，然後給齣李群胚（Lie groupoid）的概念，比較它與縴維束（fibre bundle）之間的差彆，最後給齣李代數胚（Lie algebroid）的概念，並...

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