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An introduction to noncommutative algebraic geometry
 Proceedings of the 40th Symposium on Ring Theory and Representation Theory, 53{59, Symp. Ring Theory Represent. Theory Organ. Comm
, 2008
"... Abstract. There are several research elds called noncommutative algebraic geometry. In this note, we will introduce the one founded by M. Artin. Roughly speaking, ..."
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Cited by 2 (0 self)
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Abstract. There are several research elds called noncommutative algebraic geometry. In this note, we will introduce the one founded by M. Artin. Roughly speaking,
Hopf algebras, renormalization and noncommutative geometry
 COMM. MATH. PHYS
, 1998
"... We explore the relation between the Hopf algebra associated to the renormalization of QFT and the Hopf algebra associated to the NCG computations of tranverse index theory for foliations. ..."
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Cited by 179 (12 self)
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We explore the relation between the Hopf algebra associated to the renormalization of QFT and the Hopf algebra associated to the NCG computations of tranverse index theory for foliations.
Noncommutative manifolds, the instanton algebra and isospectral deformations
 Comm. Math. Phys
"... We give new examples of noncommutative manifolds that are less standard than the NCtorus or Moyal deformations of R n. They arise naturally from basic considerations of noncommutative differential topology and have nontrivial global features. The new examples include the instanton algebra and the ..."
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Cited by 167 (29 self)
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We give new examples of noncommutative manifolds that are less standard than the NCtorus or Moyal deformations of R n. They arise naturally from basic considerations of noncommutative differential topology and have nontrivial global features. The new examples include the instanton algebra
The algebraic structure of noncommutative analytic Toeplitz algebras
 MATH.ANN
, 1998
"... The noncommutative analytic Toeplitz algebra is the wot–closed algebra generated by the left regular representation of the free semigroup on n generators. We develop a detailed picture of the algebraic structure of this algebra. In particular, we show that there is a canonical homomorphism of the a ..."
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Cited by 117 (17 self)
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The noncommutative analytic Toeplitz algebra is the wot–closed algebra generated by the left regular representation of the free semigroup on n generators. We develop a detailed picture of the algebraic structure of this algebra. In particular, we show that there is a canonical homomorphism
Noncommutative curves and noncommutative surfaces
 Bulletin of the American Mathematical Society
"... Abstract. In this survey article we describe some geometric results in the theory of noncommutative rings and, more generally, in the theory of abelian categories. Roughly speaking and by analogy with the commutative situation, the category of graded modules modulo torsion over a noncommutative grad ..."
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Cited by 91 (8 self)
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graded ring of quadratic, respectively cubic growth should be thought of as the noncommutative analogue of a projective curve, respectively surface. This intuition has lead to a remarkable number of nontrivial insights and results in noncommutative algebra. Indeed, the problem of classifying
Hopf algebras, cyclic cohomology and the transverse index theorem
 Comm. Math. Phys
, 1998
"... In this paper we present the solution of a longstanding internal problem of noncommutative geometry, namely the computation of the index of transversally elliptic operators on foliations. ..."
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Cited by 192 (20 self)
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In this paper we present the solution of a longstanding internal problem of noncommutative geometry, namely the computation of the index of transversally elliptic operators on foliations.
Feynman diagrams and lowdimensional topology
, 2006
"... We shall describe a program here relating Feynman diagrams, topology of manifolds, homotopical algebra, noncommutative geometry and several kinds of “topological physics”. The text below consists of 3 parts. The first two parts (topological sigma model and ChernSimons theory) are formally independ ..."
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Cited by 224 (3 self)
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We shall describe a program here relating Feynman diagrams, topology of manifolds, homotopical algebra, noncommutative geometry and several kinds of “topological physics”. The text below consists of 3 parts. The first two parts (topological sigma model and ChernSimons theory) are formally
ON SOME APPROACHES TOWARDS NONCOMMUTATIVE ALGEBRAIC GEOMETRY
"... The works of R. Descartes, I. M. Gelfand and A. Grothendieck have convinced us that commutative rings should be thought of as rings of functions on some appropriate (commutative) spaces. If we try to push this notion forward we reach the realm of Noncommutative Geometry. The confluence of ideas com ..."
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Cited by 1 (0 self)
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The works of R. Descartes, I. M. Gelfand and A. Grothendieck have convinced us that commutative rings should be thought of as rings of functions on some appropriate (commutative) spaces. If we try to push this notion forward we reach the realm of Noncommutative Geometry. The confluence of ideas
A BRIEF SURVEY OF NONCOMMUTATIVE ALGEBRAIC GEOMETRY
"... The works of R. Descartes, I. M. Gelfand and A. Grothendieck have convinced us that commutative rings should be thought of as rings of functions on some appropriate (commutative) spaces. If we try to push this notion forward we reach the realm of Noncommutative Geometry. The confluence of ideas com ..."
Abstract
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The works of R. Descartes, I. M. Gelfand and A. Grothendieck have convinced us that commutative rings should be thought of as rings of functions on some appropriate (commutative) spaces. If we try to push this notion forward we reach the realm of Noncommutative Geometry. The confluence of ideas
Results 1  10
of
3,184