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Cannas da Silva A., Weinstein A. — Geometric Models for Noncommutative Algebra
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Название: Geometric Models for Noncommutative AlgebraАвторы: Cannas da Silva A., Weinstein A. Аннотация: The volume is based on a course, "Geometric Models for Noncommutative Algebras" taught by Professor Weinstein at Berkeley. Noncommutative geometry is the study of noncommutative algebras as if they were algebras of functions on spaces, for example, the commutative algebras associated to affine algebraic varieties, differentiable manifolds, topological spaces, and measure spaces. In this work, the authors discuss several types of geometric objects (in the usual sense of sets with structure) that are closely related to noncommutative algebras.
Язык: Рубрика: Математика /Алгебра /Абстрактная алгебра /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1998Количество страниц: 184Добавлена в каталог: 28.02.2005Операции: Положить на полку |
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Предметный указатель
77 30 29 Action of a groupoid bisection 107 Action of a Lie algebra 8 Action, coadjoint 39 Action, effective 8 Action, free 8 Action, groupoid 90 101 Action, groupoid algebra action 103 Action, Hamiltonian 39 Action, linear action 102 Action, right 8 Adjoint operation 47 Adjoint representation of 14 Admissible section 106 Albert, C. 108 Algebra, center 50 Algebra, dual pair 50 Algebra, factor 50 Algebra, von Neumann 49 Algebra, Weyl 149 Almeida, R. 118 Almost commutativity of the universal enveloping algebra 5 Almost complex structure 120 Almost Lie algebra 7 Almost Poisson structure 12 Almost symplectic manifold 20 Anchor map, definition 113 Anchor map, image 113 Anchor map, injective 115 Anchor map, kernel 113 Anchor map, surjective 123 Antipode 69 Arnold, V. 26 Associativity of the cup product 142 Associativity, associative structure 142 Associativity, coassociativity 70 Atiyah algebra 123 Atiyah sequence 123 Atiyah, M. 121 123 Baer groupoid 91 Baer, A. 91 Berezin, F.A. 81 82 Bisection 106 107 Bivector field 12 Borel groupoid 93 Borel, E. 152 Bracket on alternating multilinear maps 142 Bracket, cobracket 132 Bracket, commutator 150 Bracket, Dirac's quantum Poisson 152 157 Bracket, E-Gerstenhaber bracket 133 Bracket, Gerstenhaber 141 Bracket, Gerstenhaber bracket on Hochschild cohomology 143 Bracket, Lie — Poisson 11 Bracket, Poisson 149 Bracket, properties of 133 Bracket, Schouten — Nijenhuis 12 135 144 Brandt groupoid 87 Brandt, W. 87 89 Bundle of groups 93 Bundle of Lie algebras 114 116 Bundle of Lie groups 116 C*-algebra, definition 47 C*-algebra, groupoid 98 Canonical 1-form 36 Canonical coordinate 14 Canonical Poisson relation 14 Canonical symplectic structure on a cotangent bundle 36 119 Cartan's magic formula 21 126 159 Cartan, E. 9 Casimir function 14 16 136 Cauchy — Riemann structure 121 Center 50 Chevalley cohomology 132 142 Chevalley complex 142 Chevalley — Eilenberg cohomology 142 Classical observables 151 Classical Yang — Baxter equation 135 Co-commutativity of the coproduct 82 Co-unit or coidentity 69 Coadjoint action 39 Coadjoint orbit 39 Coarse groupoid 87 Coboundary 43 Cobracket 132 Cochain 43 Cocycle 43 Cohomology, Chevalley 132 142 Cohomology, Chevalley — Eilenberg 142 Cohomology, de Rham 23 Cohomology, E- 136 Cohomology, E-cohomology 132 Cohomology, Gel'fand — Fuks 162 Cohomology, Harrison 142 Cohomology, Hochschild 142 Cohomology, Lie algebra 132 142 Cohomology, Lie algebroid 132 136 Cohomology, Poisson 16 Cohomology, Poisson cohomology on a Lie algebroid 136 Cohomology, squaring map 139 Coisotropic 34 Collective function 66 Commutant, definition 49 Commutant, double 50 Commutant, double commutant theorem 50 Commutant, Poisson geometry 51 Commutative Hopf algebra 72 Compact operator 48 Compatible equivalence relation 34 Complete Poisson map 31 Complete symplectically complete foliation 53 Complex coordinates in symplectic geometry 62 Complex Lie algebroid 120 Complex structure 120 Complexes, Chevalley 142 Complexes, Hochschild 142 Complexified tangent bundle 62 Connection form 124 Connection on a Lie algebroid 124 Connection on a transitive Lie algebroid 124 Connection, Ehresmann 45 Connection, Fedosov's 155 Connection, flat 44 102 Connection, flattening 156 160 Connection, iterative construction 156 160 Connection, torsionless flat Poisson 155 Connes, A. 89 Conormal space 25 Convolution of functions 75 Convolution of measures 73 98 Coproduct, co-commutativity 82 Coproduct, definition 69 CR-functions 121 CR-structure 121 Cup product of multilinear maps 142 Cup product on Hochschild cohomology 143 Cup product, associativity 142 Cup product, supercommutativity 143 Curvature, effective 160 Curvature, form 124 Curvature, Lie algebroid 124 Curvature, Weyl 160 Darboux's theorem 20 21 Dazord, P. 108 117 Deformation of products 144 Deformation of products of functions 144 146 Deformation, Lie algebra 2 Deformation, obstructions 143 Deformation, quantization 6 144 146 155 Deformation, quantization of 151 Deformation, theory 141 Degenerate Lie algebra 26 Degree of 131 Degree of 133 Degree of an E-differential form 131 Degree of an E-multivector field 132 Degree, multilinear map 141 Density, 77 Density, definition 77 Density, generalized 80 Derivation of a Poisson algebra 15 Derivation of a superalgebra xv Derivation, inner 15 157 Derivation, law for Dirac's bracket 152 Derivation, outer 15 Diagonal subgroupoid 89 Diffeological space 118 Differentiable groupoid 93 Dirac's quantum Poisson bracket 152 157 Dirac, P. 151 152 157 158 Distribution, compactly supported 79 Distribution, group algebra 76 Distributional section 79 Douady, A. 118 Dual of a Lie algebroid 119 Dual pair from complex geometry 65 Dual pair in algebra 50 Dual pair in Poisson geometry 51 Dual pair, symplectic 53 E- 136 E-cohomology 132 E-differential form, definition 131 E-differential form, degree 131 E-differential form, E-k-form 131 E-differential form, homogeneous 131 E-differential form, properties of 131 E-Gerstenhaber bracket 133 E-Lie derivative 113 133 137 E-multivector field 132 E-Poisson bivector field 135 E-symplectic form 135 E-symplectic structure 135 Effective curvature 160 Ehresmann, C. 45 92 Exact Poisson bivector field 137 Examples of a groupoid algebra 97 Examples of groupoid 89 Examples of Lie algebroids, Atiyah algebra 123 Examples of Lie algebroids, Atiyah sequence 123 Examples of Lie algebroids, bundle of Lie algebras 114 Examples of Lie algebroids, Lie algebra 114 Examples of Lie algebroids, Lie algebroid of a Lie groupoid 114 Examples of Lie algebroids, Lie algebroid of a Poisson manifold 125 Examples of Lie algebroids, Lie algebroid of a symplectic manifold 125 Examples of Lie algebroids, tangent bundle 114 Examples of Lie algebroids, transformation Lie algebroid 114 Examples of Lie algebroids, transitive Lie algebroid 123 Examples of Lie algebroids, Y-tangent bundle 127 128 Extended groupoid algebra 105 F-homotopic 94 Factor 50 Fedosov quantization 161 Fedosov, B. 154 Flat connection 45 102 Foliation, F-homotopy 94 Foliation, graph 94 Foliation, holonomy groupoid 93 Foliation, irrational 59 Foliation, leaf 93 Foliation, one-sided holonomy 95 Foliation, Reeb foliation 94 Foliation, symplectic 23 Foliation, symplectically complete 53 Formal adjoint 80 Formal Weyl algebra 150 158 Formality conjecture 144 Frobenius theorem 8 19 45 Fuchssteiner, B. 125 Function, Casimir 14 16 136 Function, collective 66 Function, Hamiltonian 40 Fundamental groupoid 89 94 Gel'fand, I. 48 General linear groupoid 102 Generalized density 80 Generalized section 79 105 Gerstenhaber algebra of a Lie algebroid 133 Gerstenhaber algebra, definition 133 Gerstenhaber algebra, E-Gerstenhaber algebra 133 Gerstenhaber algebra, E-Gerstenhaber bracket 133 Gerstenhaber, M. 134 141 Ginzburg, V. 57 Grading formal Weyl algebra 158 Grading universal enveloping algebra 3 Graph 94 Grothendieck, A. 89 Group algebra, distribution 76 Group algebra, distribution group algebra 76 Group algebra, group(-element)-like 74 Group algebra, list of structures 73 Group algebra, measure 73 Group, definition xvi 87 Group, isotropy subgroup 89 Groupoid action 90 101 Groupoid action of a bisection 107 Groupoid as a category xvi Groupoid with structure 92 Groupoid, Baer groupoid 91 Groupoid, Borel 93 Groupoid, Brandt groupoid 87 Groupoid, bundle of groups 93 Groupoid, bundle of Lie algebras 116 Groupoid, bundle of Lie groups 116 Groupoid, C* -algebra 98 Groupoid, coarse groupoid 87 Groupoid, comparison with group xvi Groupoid, definition 85 Groupoid, diagonal subgroupoid 89 Groupoid, differentiable 93 Groupoid, ergodic theory 89 Groupoid, example of a groupoid algebra 97 Groupoid, examples 89 Groupoid, extended groupoid algebra 105 Groupoid, fundamental 89 Groupoid, fundamental groupoid 94 Groupoid, Galois theory 89 Groupoid, general linear groupoid 102 Groupoid, groupoid algebra 98 Groupoid, groupoid algebra action 103 Groupoid, groupoid algebra with coeficients in a vector bundle 103 Groupoid, Haar system 98 Groupoid, holonomy of a foliation 93 Groupoid, identity section 85 Groupoid, intrinsic groupoid algebra 99 Groupoid, inversion 86 Groupoid, isotropy subgroupoid 89 Groupoid, left invariant vector field 111 Groupoid, Lie 93 Groupoid, measurable 93 Groupoid, morphism 88 Groupoid, normal bundle of G(0) 100 Groupoid, orbit 89 Groupoid, pair groupoid 87 94 Groupoid, principal groupoid 90 Groupoid, product 85 Groupoid, product of groupoids 87 Groupoid, relation 88 Groupoid, representation 102
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