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Noncommutative proj and coherent algebras
 Math. Res. Lett
"... Abstract. We prove that an abelian category equipped with an ample sequence of objects is equivalent to the quotient of the category of coherent modules over the corresponding algebra by the subcategory of finitedimensional modules. In the Noetherian case a similar result was proved by Artin and Zh ..."
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Cited by 11 (0 self)
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Abstract. We prove that an abelian category equipped with an ample sequence of objects is equivalent to the quotient of the category of coherent modules over the corresponding algebra by the subcategory of finitedimensional modules. In the Noetherian case a similar result was proved by Artin and Zhang in [2].
Noncommutative instantons and twistor transform
 Commun. Math. Phys
"... Recently N. Nekrasov and A. Schwarz proposed a modification of the ADHM construction of instantons which produces instantons on a noncommutative deformation of R4. In this paper we study the relation between their construction and algebraic bundles on noncommutative projective spaces. We exhibit one ..."
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Cited by 54 (4 self)
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Recently N. Nekrasov and A. Schwarz proposed a modification of the ADHM construction of instantons which produces instantons on a noncommutative deformation of R4. In this paper we study the relation between their construction and algebraic bundles on noncommutative projective spaces. We exhibit
Maps between noncommutative spaces
, 2000
"... Abstract. Let J be a graded ideal in a not necessarily commutative graded kalgebra A = A0 ⊕A1 ⊕ · · · in which dimk Ai < ∞ for all i. We show that the map A → A/J induces a closed immersion i: Proj nc A/J → Proj nc A between the noncommutative projective spaces with homogeneous coordinate rin ..."
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Cited by 4 (1 self)
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Abstract. Let J be a graded ideal in a not necessarily commutative graded kalgebra A = A0 ⊕A1 ⊕ · · · in which dimk Ai < ∞ for all i. We show that the map A → A/J induces a closed immersion i: Proj nc A/J → Proj nc A between the noncommutative projective spaces with homogeneous coordinate
Serre duality for noncommutative projective schemes
 Proc. Amer. Math. Soc
, 1997
"... Abstract. We prove the Serre duality theorem for the noncommutative projective scheme proj A when A is a graded noetherian PI ring or a graded noetherian ASGorenstein ring. Let k be a eld and let A = L i0 Ai be an Ngraded right noetherian kalgebra. In this paper we always assume that A is locall ..."
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Cited by 30 (8 self)
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Abstract. We prove the Serre duality theorem for the noncommutative projective scheme proj A when A is a graded noetherian PI ring or a graded noetherian ASGorenstein ring. Let k be a eld and let A = L i0 Ai be an Ngraded right noetherian kalgebra. In this paper we always assume that A
Noncommutative geometry of tilings and gap labelling
 Rev. Math. Phys
, 1995
"... To a given tiling a non commutative space and the corresponding C ∗algebra are constructed. This includes the definition of a topology on the groupoid induced by translations of the tiling. The algebra is also the algebra of observables for discrete models of one or many particle systems on the til ..."
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Cited by 53 (13 self)
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To a given tiling a non commutative space and the corresponding C ∗algebra are constructed. This includes the definition of a topology on the groupoid induced by translations of the tiling. The algebra is also the algebra of observables for discrete models of one or many particle systems on the tiling or its periodic identification. Its scaled ordered K0group furnishes the gap labelling of Schrödinger operators. The group is computed for one dimensional tilings and Cartesian products thereof. Its image under a state is investigated for tilings which are invariant under a substitution. Part of this image is given by an invariant measure on the hull of the tiling which is determined. The results from the Cartesian products of one dimensional tilings point out that the gap labelling by means of the values of the integrated density of states is already fully determined by this measure.
Naïve Noncommutative Blowups . . .
"... In an earlier paper [KRS] we defined and investigated the properties of the naïve blowup of an integral projective scheme X at a single closed point. In this paper we extend those results to the case when one naïvely blows up X at any suitably generic zerodimensional subscheme Z. The resulting alge ..."
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Cited by 18 (9 self)
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over X. These results are used in the companion paper [RS1] to prove that a large class of noncommutative surfaces can be written as naïve blowups.
NONCOMMUTATIVE ALGEBRAIC GEOMETRY AND THE STUDY OF NONCOMMUTATIVE TORI
, 2008
"... I would like to thank all the organizers of the International Workshop on Noncommutative Geometry, 2005 for giving me this opportunity to speak. In section 1 we shall browse through some interesting definitions and constructions which will be referred to later on. In section 2 we shall deal with non ..."
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I would like to thank all the organizers of the International Workshop on Noncommutative Geometry, 2005 for giving me this opportunity to speak. In section 1 we shall browse through some interesting definitions and constructions which will be referred to later on. In section 2 we shall deal
The geometry of arithmetic noncommutative projective lines
 J. Algebra
"... Abstract. Let k be a perfect eld and let K=k be a nite extension of elds. An arithmetic noncommutative projective line is a noncommutative space of the form ProjSK(V), where V be a kcentral twosided vector space over K of rank two and SK(V) is the noncommutative symmetric algebra generated by V ov ..."
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Cited by 3 (3 self)
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Abstract. Let k be a perfect eld and let K=k be a nite extension of elds. An arithmetic noncommutative projective line is a noncommutative space of the form ProjSK(V), where V be a kcentral twosided vector space over K of rank two and SK(V) is the noncommutative symmetric algebra generated by V
Results 1  10
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1,057