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Noncommutative differential calculus, homotopy . . .
, 2000
"... We define a notion of a strong homotopy BV algebra and apply it to deformation theory problems. Formality conjectures for Hochschild cochains are formulated. We prove several results supporting these conjectures. ..."
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Cited by 57 (1 self)
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We define a notion of a strong homotopy BV algebra and apply it to deformation theory problems. Formality conjectures for Hochschild cochains are formulated. We prove several results supporting these conjectures.
One noncommutative differential calculus coming from the inner derivation, preprint
"... Abstract. We define a noncommutative differential calculus constructed from the inner derivation, then several relevant examples are showed. It is of interest to note that for certain C ∗algebra, this calculus is closely related to the classical one when the algebra associates a deformation paramet ..."
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Cited by 2 (1 self)
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Abstract. We define a noncommutative differential calculus constructed from the inner derivation, then several relevant examples are showed. It is of interest to note that for certain C ∗algebra, this calculus is closely related to the classical one when the algebra associates a deformation
NONCOMMUTATIVE DIFFERENTIAL CALCULUS ABSTRACT ON THE κMINKOWSKI SPACE
, 1994
"... Following the construction of the κMinkowski space from the bicrossproduct structure of the κPoincare group, we investigate possible differential calculi on this noncommutative space. We discuss then the action of the Lorentz quantum algebra and prove that there are no 4D bicovariant differential ..."
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Following the construction of the κMinkowski space from the bicrossproduct structure of the κPoincare group, we investigate possible differential calculi on this noncommutative space. We discuss then the action of the Lorentz quantum algebra and prove that there are no 4D bicovariant differential
An Example of ZN–Graded Noncommutative Differential Calculus
, 1999
"... In this work, we consider the algebra MN(C) of N × N matrices as a cyclic quantum plane. We also analyze the coaction of the quantum group F and the action of its dual quantum algebra H on it. Then, we study the decomposition of MN(C) in terms of the quantum algebra representations. Finally, we deve ..."
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develop the differential algebra of the cyclic group ZN with d N = 0, and treat the particular In the last decade, the concept of the noncommutative differential geometry, [1] has been extensively developed. The most simple example of noncommutative differential geometry based on derivations is given
Noncommutative Differential Calculus for Dbrane in NonConstant B Field Background
, 2001
"... In this paper we try to construct noncommutative YangMills theory for generic Poisson manifolds. It turns out that the noncommutative differential calculus defined in an old work is exactly what we need. Using this calculus, we generalize results about the SeibergWitten map, the DiracBornInfeld ..."
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Cited by 13 (0 self)
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In this paper we try to construct noncommutative YangMills theory for generic Poisson manifolds. It turns out that the noncommutative differential calculus defined in an old work is exactly what we need. Using this calculus, we generalize results about the SeibergWitten map, the Dirac
RELATIVISTIC KINETIC MOMENTUM OPERATORS, HALFRAPIDITIES AND NONCOMMUTATIVE DIFFERENTIAL CALCULUS
"... It is shown that the generating function for the matrix elements of irreps of the Lorentz group is the common eigenfunction of the interior derivatives of the noncommutative differential calculus over the commutative algebra generated by the coordinate functions in the Relativistic Conˇguration Spa ..."
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It is shown that the generating function for the matrix elements of irreps of the Lorentz group is the common eigenfunction of the interior derivatives of the noncommutative differential calculus over the commutative algebra generated by the coordinate functions in the Relativistic Conˇguration
Noncommutative differential calculus and the axial anomaly in abelian lattice gauge theories
 Nucl. Phys. B
"... The axial anomaly in lattice gauge theories has a topological nature when the Dirac operator satisfies the GinspargWilson relation. We study the axial anomaly in Abelian gauge theories on an infinite hypercubic lattice by utilizing cohomological arguments. The crucial tool in our approach is the no ..."
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Cited by 15 (2 self)
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is the noncommutative differential calculus (NCDC) which makes the Leibniz rule of exterior derivatives valid on the lattice. The topological nature of the “Chern character ” on the lattice becomes manifest in the context of NCDC. Our result provides an algebraic proof of Lüscher’s theorem for a four
Noncommutative differential calculus: quantum groups, stochastic processes, and the antibracket
 IN THE PROCEEDING OF THE XXII CONFERENCE ON DIFFERENTIAL GEOMETRIC METHODS IN THEORETICAL PHYSICS
, 1993
"... We explore a differential calculus on the algebra of C∞functions on a manifold. The former is ‘noncommutative’ in the sense that functions and differentials do not commute, in general. Relations with bicovariant differential calculus on certain quantum groups and stochastic calculus are discussed. ..."
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Cited by 2 (2 self)
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We explore a differential calculus on the algebra of C∞functions on a manifold. The former is ‘noncommutative’ in the sense that functions and differentials do not commute, in general. Relations with bicovariant differential calculus on certain quantum groups and stochastic calculus are discussed
unknown title
, 2005
"... Separation of noncommutative differential calculus on quantum Minkowski space ..."
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Separation of noncommutative differential calculus on quantum Minkowski space
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