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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 12 (2 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
SU(n)connections and noncommutative differential geometry
 J. Geom. Phys
, 1998
"... We study the noncommutative differential geometry of the algebra of endomorphisms of any SU(n)vector bundle. We show that ordinary connections on such SU(n)vector bundle can be interpreted in a natural way as a noncommutative 1form on this algebra for the differential calculus based on derivation ..."
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Cited by 11 (4 self)
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We study the noncommutative differential geometry of the algebra of endomorphisms of any SU(n)vector bundle. We show that ordinary connections on such SU(n)vector bundle can be interpreted in a natural way as a noncommutative 1form on this algebra for the differential calculus based on derivations. We interpret the Lie algebra of derivations of the algebra of endomorphisms as a Lie algebroid. Then we look at noncommutative connections as generalizations of these usual connections.
Submanifolds and Quotient Manifolds in Noncommutative Geometry
 J. Math. Phys
, 1996
"... We define and study noncommutative generalizations of submanifolds and quotient manifolds, for the derivationbased differential calculus introduced by M. DuboisViolette and P. Michor. We give examples to illustrate these definitions. ..."
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Cited by 8 (5 self)
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We define and study noncommutative generalizations of submanifolds and quotient manifolds, for the derivationbased differential calculus introduced by M. DuboisViolette and P. Michor. We give examples to illustrate these definitions.
Comments About Higgs Field, Noncommutative Geometry and the Standard Model
 MARSEILLE PREPRINT CPT95 /P.3184 AND HEPTH/9505192
, 1995
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More on the FrölicherNijenhuis Bracket In Non Commutative Differential Geometry
, 1996
"... . In commutative differential geometry the FrolicherNijenhuis bracket computes all kinds of curvatures and obstructions to integrability. In [1] the FrolicherNijenhuis bracket was developed for universal differential forms of noncommutative algebras, and several applications were given. In this pa ..."
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Cited by 6 (3 self)
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. In commutative differential geometry the FrolicherNijenhuis bracket computes all kinds of curvatures and obstructions to integrability. In [1] the FrolicherNijenhuis bracket was developed for universal differential forms of noncommutative algebras, and several applications were given. In this paper this bracket and the FrolicherNijenhuis calculus will be developed for several kinds of differential graded algebras based on derivations, which were introduced by [6]. Table of contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Convenient vector spaces . . . . . . . . . . . . . . . . . . . . . . 3 3. Preliminaries: graded differential algebras, derivations, and operations of Lie algebras . . . . . . . . . . . . . . . . . . . . 6 4. Derivations on universal differential forms . . . . . . . . . . . . . . . 8 5. The FrolicherNijenhuis calculus on Chevalley type cochains . . . . . . . 11 6. Description of all derivations in the Chevalley differential...
Connections on Central Bimodules
, 1995
"... We define and study the theory of derivationbased connections on a recently introduced class of bimodules over an algebra which reduces to the category of modules whenever the algebra is commutative. This theory contains, in particular, a noncommutative generalization of linear connections. We also ..."
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Cited by 6 (1 self)
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We define and study the theory of derivationbased connections on a recently introduced class of bimodules over an algebra which reduces to the category of modules whenever the algebra is commutative. This theory contains, in particular, a noncommutative generalization of linear connections. We also discuss the different noncommutative versions of differential forms based on derivations. Then we investigate reality conditions and a noncommutative generalization of pseudoriemannian structures.
Lectures On Alain Connes' Non Commutative Geometry And Applications To Fundamental Interactions
, 1994
"... We introduce the reader to Alain Connes non commutative differential geometry, and sketch the applications made to date to (the lagrangian level of) fundamental physical interactions. ..."
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Cited by 5 (1 self)
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We introduce the reader to Alain Connes non commutative differential geometry, and sketch the applications made to date to (the lagrangian level of) fundamental physical interactions.
Examples of derivationbased differential calculi related to noncommutative gauge theories
 INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
, 2008
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THE FRÖLICHERNIJENHUIS BRACKET FOR DERIVATION BASED NON COMMUTATIVE DIFFERENTIAL FORMS
, 1994
"... In commutative differential geometry the FrölicherNijenhuis bracket computes all kinds of curvatures and obstructions to integrability. In [3] the FrölicherNijenhuis bracket was developped for universal differential forms of noncommutative algebras, and several applications were given. In this p ..."
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Cited by 2 (2 self)
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In commutative differential geometry the FrölicherNijenhuis bracket computes all kinds of curvatures and obstructions to integrability. In [3] the FrölicherNijenhuis bracket was developped for universal differential forms of noncommutative algebras, and several applications were given. In this paper this bracket and the FrölicherNijenhuis calculus will be developped for several kinds of differential graded algebras based on derivations, which were indroduced by [6].