zbMath0681.55004MaRDI QIDQ4730462
Alain Connes
Publication date: 1987
Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Stochastic self-similar and fractal universe ⋮
Varying G, accelerating universe, and other relevant consequences of a stochastic self-similar and fractal universe ⋮
Getzler rescaling via adiabatic deformation and a renormalized index formula ⋮
Transverse noncommutative geometry of foliations ⋮
Integrability and positivity in quantum field theory on noncommutative geometry ⋮
Diagonal-preserving isomorphisms of étale groupoid algebras ⋮
Trees and ultrametric spaces: A categorical equivalence ⋮
Multiple noncommutative tori as quantum symmetry groups ⋮
Introduction to Dubois-Violette's noncommutative differential geometry ⋮
Duality for logarithmic interpolation spaces when \(0<q < 1\) and applications ⋮
Supersymmetry and noncommutative geometry ⋮
Descent equations of Yang-Mills anomalies in noncommutative geometry ⋮
Quantum Riemannian geometry of quantum projective spaces ⋮
Algebraic index theorem ⋮
On the structure of a differential algebra used by Connes and Lott ⋮
Quantum principal bundles and Tannaka-Krein duality theory ⋮
Morphisms from \(U_v(sl_2)\) to the rotation algebra \({\mathcal A}_\theta\) ⋮
Principal measures and spectral shift measures associated with Dixmier traces ⋮
Spontaneous symmetry breaking and geometry from the spectral viewpoint ⋮
The modular automorphism group of a Poisson manifold ⋮
Spin-statistics and CPT theorems in noncommutative field theory ⋮
A note on extrapolation theory ⋮
YM on the dielectric brane: a D0-brane tale ⋮
Covariant connections on bicovariant differential calculus ⋮
\(K\)-duality for pseudomanifolds with an isolated singularity. ⋮
Analyticity and forward dispersion relations in noncommutative quantum field theory ⋮
Doubly \(\Lambda\)-commuting row isometries, universal models, and classification ⋮
A Hilbert bundle description of differential \(K\)-theory ⋮
Noncommutative geodesics and the KSGNS construction ⋮
Dirac operators on noncommutative hypersurfaces ⋮
Differentiable functions of quaternion variables. ⋮
Atlas of quasicrystalline tilings. ⋮
Derivation of the threshold and absolute temperature T\(_c=\)273.16 K from the topology of quantum space-time. ⋮
Maximal acceleration in non-commutative space-time and its implications ⋮
Connes' tangent groupoid and strict quantization ⋮
On the uncertainty of Cantorian geometry and the two-slit experiment ⋮
A dual formula for the spectral distance in noncommutative geometry ⋮
On the computation of quantum characteristic exponents. ⋮
Dynamic noncommutative BTZ black holes ⋮
Quantum Koszul formula on quantum spacetime ⋮
Spectral triples and wavelets for higher-rank graphs ⋮
Fantappié's group as an extension of special relativity on \({\mathcal E}^{(\infty)}\) Cantorian space-time ⋮
Dynamical origin of the \(\star_\theta \)-noncommutativity in field theory from quantum mechanics ⋮
Self-similar and oscillating solutions of Einstein's equation and other relevant consequences of a stochastic self-similar and fractal universe via El Naschie's \(\varepsilon^{(\infty)}\) Cantorian space-time ⋮
Waveguiding and mirroring effects in stochastic self-similar and Cantorian \({\mathcal E}^{(\infty)}\) universe ⋮
Dynamical systems on El Naschie's \({\mathcal E}^{(\infty)}\) Cantorian space-time ⋮
Fractal Cantorian structures with spatial pseudo-spherical symmetry for a possible description of the actual segregated universe as a consequence of its primordial fluctuations ⋮
Ergodic actions of \(S_\mu U(2)\) on \(C^{*}\)-algebras from \(II_{1}\) subfactors ⋮
Equivalence between the Morita categories of étale Lie groupoids and of locally grouplike Hopf algebroids ⋮
Heat equation in a model matrix geometry ⋮
The Helton-Howe trace formula for submodules ⋮
Matrix revolutions: an introduction to quantum variables for young mathematicians ⋮
Kazhdan projections, random walks and ergodic theorems ⋮
Spin geometry of the rational noncommutative torus ⋮
Relating diffraction and spectral data of aperiodic tilings: towards a Bloch theorem ⋮
Metric approximations of spectral triples on the Sierpiński gasket and other fractal curves ⋮
Analytic and algebraic indices of elliptic operators associated with discrete groups of quantized canonical transformations ⋮
Gauge invariant energy spectra in 2-dimensional noncommutative quantum mechanics ⋮
Super Dirac operator on the super fuzzy sphere \(S_F^{(2|2)}\) in instanton sector using super Ginsparg-Wilson algebra ⋮
On the irreducibility of spatial ambiguity in quantum physics ⋮
Penrose universe and Cantorian spacetime as a model for noncommutative quantum geometry ⋮
Knot theory in \(\mathbb{R}^4\) and the Hausdorff dimension of a quantum path in \({\mathcal E}^{(\infty)}\) ⋮
The fractal dimension of spacetime. -- Remarks on theoretical derivation and experimental verification. ⋮
On the Lefschetz problem in noncommutative geometry. ⋮
The Baum-Connes assembly map, delocalization and the Chern character ⋮
Products in Hochschild cohomology and Grothendieck rings of group crossed products. ⋮
On unbounded \(p\)-summable Fredholm modules ⋮
General frame structures on quantum principal bundles ⋮
Is quantum space-time infinite dimensional ⋮
Projections over quantum homogeneous odd-dimensional spheres ⋮
Mapping properties of operator-valued pseudo-differential operators ⋮
The lattice coordinatized by a ring ⋮
Fourier analysis for type III representations of the noncommutative torus ⋮
Noncommutative Kähler structure on \(C^\ast\)-dynamical systems ⋮
Currents on Grassmann algebras ⋮
A groupoid approach to pseudodifferential calculi ⋮
Local index formulae on noncommutative orbifolds and equivariant zeta functions for the affine metaplectic group ⋮
Functoriality of groupoid quantales. I. ⋮
Noncommutative supergeometry, duality and deformations ⋮
Noncommutative Calabi-Yau manifolds ⋮
Topological charges of noncommutative soliton ⋮
Tachyon condensation on fuzzy sphere and noncommutative solitons ⋮
Noncommutative K3 surfaces ⋮
Real dimensional spaces in noncommutative geometry ⋮
Scale type \((N,N)\) and an order-based topology induced on the automorphism group ⋮
Computation of the gap-labelling for quasi-crystals ⋮
Trace invariants associated with quotient modules of the Hardy module ⋮
The status and programs of scale relativity theory ⋮
Operators on spaces of analytic functions belonging to \({\mathcal L}^{(1,\infty)}\) ⋮
Riemann-Roch theorems via deformation quantization. II ⋮
\(O(3)\) sigma model with Hopf term on fuzzy sphere ⋮
An integrable noncommutative version of the sine-Gordon system ⋮
Spectral flow and Dixmier traces ⋮
Spectral invariance of algebras of pseudodifferential operators ⋮
Noncommutative geometry and spacetime gauge symmetries of string theory ⋮
Topological symmetry, background independence and matrix models ⋮
Towards a background independent approach to \(\mathcal M\) theory ⋮
Comments on the Riemann conjecture and index theory on Cantorian fractal space-time. ⋮
Wild topology, hyperbolic geometry and fusion algebra of high energy particle physics ⋮
The Heisenberg calculus, index theory and cyclic cohomology
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