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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 22 (3 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 13 (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
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...
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].
CONNECTIONS OVER TWISTED TENSOR PRODUCTS OF ALGEBRAS
, 2006
"... Abstract. Motivated from some results in classical differential geometry, we give a constructive procedure for building up a connection over a (twisted) tensor product of two algebras, starting from connections defined on the factors. The curvature for the product connection is explicitly calculated ..."
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Abstract. Motivated from some results in classical differential geometry, we give a constructive procedure for building up a connection over a (twisted) tensor product of two algebras, starting from connections defined on the factors. The curvature for the product connection is explicitly calculated, and shown to be independent of the choice of the twisting map and the module twisting map used to define the product connection. As a consequence, we obtain that a product of two flat connections is again a flat connection. We show that our constructions also behves well with respesct to bimodule structures, namely being the product of two bimodule connections again a bimodule connection. As an application of our theory, all the product connections on the quantum plane are computed.