An invitation to dyslectic geometry
type: Item
instance of: scholarly article
title: An invitation to dyslectic geometry
zbMATH Open document ID: 0791.58013
published in: Journal of Algebra
publication date: 1993-05-16T00:00:00Z
review text: ``Dyslectic geometry is a ``\(G\)-commutative'' geometry generalizing the physicists' \(\mathbb{Z}/2\mathbb{Z}\)-commutative supergeometry to the case of an arbitrary group \(G\)\dots'' After defining the notion of \(G\)-commutative \(G\)-algebra and sketching the general theory of such objects, the author provides some examples (Connes' \(C^ \ast\)-algebra associated with the Kronecker flow on the torus, certain algebras constructed from non-Archimedean local fields, superalgebras, etc.). Then the author undertakes the construction of a theory of \(G\)-schemes: a \(\text{Spec}\) functor is introduced, together with the notion of locally ringed \(G\)-space. Such objects are shown to admit an infinitesimal theory of differentials and a global cohomology theory. This interesting paper proposes an avenue for the development of a noncommutative geometry which is closer in spirit to standard algebraic geometry than Connes' approach.
Mathematics Subject Classification ID: 46L85
Mathematics Subject Classification ID: 46L87
Mathematics Subject Classification ID: 14A22
zbMATH DE Number: 169087
zbMATH Keywords: noncommutative geometry
author: Shai Haran
MaRDI profile type: Publication
full work available at URL: jabr.1993.1054
OpenAlex ID: W2016978226
DOI: 10.1006/JABR.1993.1054
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description: scientific article; zbMATH DE number 169087