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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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Rank of a Poisson structure 18 Rank, Poisson structure with constant rank 17 20 Realization, injective 59 Realization, submersive 60 Realization, symplectic 59 Reeb foliation 94 Reeb, G. 94 Regular equivalence relation 34 Regular Poisson manifold, definition 17 Regular Poisson manifold, holonomy 24 Relation 88 Representation of a groupoid 102 Representation, pointwise faithful 8 Representation, representation equivalent 56 Rinehart, G. 115 Schouten — Nijenhuis bracket 12 135 Schroedinger, E. 151 Section of the normal bundle 109 Section, admissible section 106 Section, bisection 106 Section, distributional 79 Section, generalized 79 105 Semigroup 87 106 107 Smale, S. 42 Souriau, J.-M. 42 118 Spectrum 48 Splitting theorem 19 Squaring map 139 142 143 Strong topology 48 Structure constant 8 Structure function for a Lie algebroid 119 Structure function, definition 13 Structure function, transverse structure 24 Subgroup, isotropy 89 Subgroupoid as a relation 88 Subgroupoid, definition 88 Subgroupoid, diagonal 89 Subgroupoid, isotropy 89 Subgroupoid, wide 88 Submanifold, Poisson 36 Super-commutativity xiv Super-commutativity of cup product 143 Super-derivation xv Super-Jacobi identity 133 141 142 Super-Leibniz identity 133 134 Super-Lie algebra 133 Super-manifold 131 Super-space xv Super-vector field 132 Symmetric algebra 1 Symmetric group 3 143 Symmetric tensor 3 Symmetrization 3 Symplectic, almost symplectic manifold 20 Symplectic, canonical coordinates 14 Symplectic, canonical structure on a cotangent bundle 36 119 Symplectic, Darboux's theorem 20 21 Symplectic, definition of symplectic structure 14 Symplectic, dual pair 53 Symplectic, E-symplectic form 135 Symplectic, E-symplectic structure 135 Symplectic, foliation 23 Symplectic, form 20 Symplectic, groupoid 127 Symplectic, leaf 23 Symplectic, Lie algebroid of a symplectic manifold 125 Symplectic, manifold 20 Symplectic, Poisson cohomology 23 Symplectic, realization 32 59 Symplectic, symplectically complete foliation 53 Tangent bundle as a Lie algebroid 114 Tangent bundle, complexified 62 Tensor algebra 1 Theorem, Darboux's 20 21 Theorem, double commutant 50 Theorem, Gel'fand — Naimark 48 Theorem, Lie's 17 Theorem, Splitting 19 Theorem, unique Haar measure 74 Topological groupoid 92 Topology of convergence of matrix elements 49 Topology of pointwise convergence 48 Topology on bounded operators 47 48 Topology, norm 47 Topology, strong 48 Topology, weak 49 Torus, irrational foliation 59 Torus, maximal 91 Torus, quantum 152 Transformation, groupoid 90 Transformation, Lie algebroid 114 Transitive groupoid 89 Transitive Lie algebroid 123 124 Translation maps 76 Transverse Lie algebra 24 Transverse Poisson structure 24 Transverse structure function 24 Uncertainty principle xvi Unimodular group 75 Unit or identity 69 Unital 49 Universal algebra 1 Universal enveloping algebra, almost commutativity 5 Universal enveloping algebra, definition 1 Universal enveloping algebra, grading 3 Universal enveloping algebra, Poisson bracket 5 Universal property 1 Vector field, 29 Vector field, Hamiltonian 14 20 Vector field, left invariant 111 Vector field, odd xv Vector field, Poisson 15 Vector field, set of hamiltonian vector fields 40 Vector field, set of Poisson vector fields 40 Vector fields tangent to a hypersurface 127 Vector fields tangent to the boundary 128 von Neumann algebra 49 von Neumann, J. 47 50 151 Weak topology 49 Weinstein, A. 19 26 33 34 126 Weyl algebra, afine invariance 152 Weyl algebra, automorphism 153 Weyl algebra, bundle 153 Weyl algebra, definition 149 Weyl algebra, derivation 152 Weyl algebra, filtration 158 Weyl algebra, flat connection 154 Weyl algebra, formal 150 158 Weyl algebra, Moyal — Weyl product 149 150 Weyl algebra, Weyl product 150 Weyl curvature 160 Weyl group 91 Weyl groupoid 91 Weyl product 150 Weyl symbol 151 Xu, P. 56 Y-tangent bundle 127 Yang — Baxter equation 135
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