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Lectures on graded differential algebras and noncommutative geometry
, 1999
"... These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new developments. ..."
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Cited by 49 (5 self)
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These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new developments.
Some Aspects of Noncommutative Differential Geometry
"... We discuss in some generality aspects of noncommutative differential geometry associated with reality conditions and with differential calculi. We then describe the differential calculus based on derivations as generalization of vector fields, and we show its relations with quantum mechanics. Finall ..."
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Cited by 18 (1 self)
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We discuss in some generality aspects of noncommutative differential geometry associated with reality conditions and with differential calculi. We then describe the differential calculus based on derivations as generalization of vector fields, and we show its relations with quantum mechanics. Finally we formulate a general theory of connections in this framework. 1
Comments About Higgs Field, Noncommutative Geometry and the Standard Model
 MARSEILLE PREPRINT CPT95 /P.3184 AND HEPTH/9505192
, 1995
"... ..."
and
, 2008
"... We analyse the structure of the κ = 0 limit of a family of algebras Aκ describing noncommutative versions of spacetime, with κ a parameter of noncommutativity. Assuming the Poincaré covariance of the κ = 0 limit, we show that, besides the algebra of functions on Minkowski space, A0 must contain a n ..."
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We analyse the structure of the κ = 0 limit of a family of algebras Aκ describing noncommutative versions of spacetime, with κ a parameter of noncommutativity. Assuming the Poincaré covariance of the κ = 0 limit, we show that, besides the algebra of functions on Minkowski space, A0 must contain a nontrivial extra factor AI 0 which is Lorentz covariant and which does not commute with the functions whenever it is not commutative. We give a general description of the possibilities and analyse some representative examples. 1
and
, 2008
"... We analyse the structure of the κ = 0 limit of a family of algebras Aκ describing noncommutative versions of spacetime, with κ a parameter of noncommutativity. Assuming the Poincaré covariance of the κ = 0 limit, we show that, besides the algebra of functions on Minkowski space, A0 must contain a n ..."
Abstract
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We analyse the structure of the κ = 0 limit of a family of algebras Aκ describing noncommutative versions of spacetime, with κ a parameter of noncommutativity. Assuming the Poincaré covariance of the κ = 0 limit, we show that, besides the algebra of functions on Minkowski space, A0 must contain a nontrivial extra factor AI 0 which is Lorentz covariant and which does not commute with the functions whenever it is not commutative. We give a general description of the possibilities and analyse some representative examples. 1