Noncommutative geometry and quiver algebras
type: Item
instance of: scholarly article
title: Noncommutative geometry and quiver algebras
zbMATH Open document ID: 1111.53066
author: William Crawley-Boevey
author: Victor Ginzburg
author: Pavel Etingof
published in: Advances in Mathematics
publication date: 2007-02-12T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0502301
review text: 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.
Mathematics Subject Classification ID: 53D17
Mathematics Subject Classification ID: 58J42
zbMATH DE Number: 5123974
zbMATH Keywords: noncommutative geometry
zbMATH Keywords: symplectic geometry
zbMATH Keywords: Hamiltonian reduction
reviewed by: Angela Gammella-Mathieu
MaRDI profile type: Publication
OpenAlex ID: W2153521840
Wikidata QID: Q101542442
arXiv ID: math/0502301
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DOI: 10.1016/J.AIM.2006.05.004
description: scientific article