1. Quantum metrics from length functions on quantum groups
   2025/03/03 by Are Austad, Austad, Are, David Kyed +1 · 2 citations
   Mathematics · #46L89 #58B32 #58B34 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA)
2. Multiple operator integrals, pseudodifferential calculus, and asymptotic expansions
   2024/04/25 by Hekkelman, Eva-Maria, McDonald, Edward, van Nuland, Teun D. H. · 2 citations
   #47A55 #47A60 #47F10 #47G30 #58B34 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Spectral Theory (math.SP)
3. Collapse in Noncommutative Geometry and Spectral Continuity
   2024/03/30 by Carla Farsi, Frédéric Latrémolière, Farsi, Carla +1 · 1 citation
   Physics and Astronomy · Mathematics · #46L30 #58B34 #FOS: Mathematics #Operator Algebras (math.OA)
4. Fermion integrals for finite spectral triples
   2024/03/27 by Barrett, John W. · 1 citation
   #58B34 #81T75 #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
5. Existence and uniqueness of the Levi-Civita connection on noncommutative differential forms
   2024/03/20 by Mesland, Bram, Rennie, Adam · 1 citation
   #58B34 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Quantum Algebra (math.QA)
6. Quantum Gromov-Hausdorff propinquity convergence of Christensen-Ivan quantum metrics on AF algebras
   2023/12/27 by Clay Adams, Konrad Aguilar, Adams, Clay +7 · 1 citation
   Computer Science · Mathematics · #46L30 #58B34 #Advanced Algebra and Logic #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Primary: 46L89
7. Quantum metrics on crossed products with groups of polynomial growth
   2023/12/19 by Are Austad, Jens Kaad, Austad, Are +3 · 1 citation
   Mathematics · Physics and Astronomy · #46L55 #47L65 #58B34 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #Operator Algebras (math.OA)
8. External products of spectral metric spaces
   2023/04/08 by Kaad, Jens · 1 citation
   #58B34 #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)
9. Local invariants of conformally deformed non-commutative tori II: multiple operator integrals
   2023/03/08 by van Nuland, Teun D. H., Sukochev, Fedor, Zanin, Dmitriy · 1 citation
   #46L87 #58B34 #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Spectral Theory (math.SP)
10. Jet Functors in Noncommutative Geometry
    2022/04/26 by Flood, Keegan J., Mantegazza, Mauro, Winther, Henrik · 1 citation
    #16E45 #16S32 #20G42 #58B32 #58B34 #81R60 #Differential Geometry (math.DG) #FOS: Mathematics #Primary 58A20 #Quantum Algebra (math.QA) #Secondary 47F05
11. Index theory of hypoelliptic operators on Carnot manifolds
    2022/03/09 by Goffeng, Magnus, Kuzmin, Alexey · 4 citations
    #19K33 #19K56 (primary) #22E25 #53A40 #58B34 #58J40 #58J42 (secondary) #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #Representation Theory (math.RT)
12. Estimating noncommutative distances on graphs
    2021/05/19 by Besnard, Fabien · 1 citation
    #05C99 #58B34 #Combinatorics (math.CO) #FOS: Mathematics #Operator Algebras (math.OA)
13. Finite spectral triples for the fuzzy torus
    2019/08/19 by Barrett, John W., Gaunt, James · 1 citation
    #58B34 #81T75 #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)
14. Inductive limits of C*-algebras and compact quantum metrics spaces
    2018/07/27 by Aguilar, Konrad · 1 citation
    #46L30 #46L89 #58B34 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)
15. A C^*-algebraic approach to the principal symbol II
    2018/06/19 by Sukochev, Fedor, McDonald, Edward, Zanin, Dmitriy · 1 citation
    #58B34 #58J40 #FOS: Mathematics #Operator Algebras (math.OA)
16. Duality of Gabor frames and Heisenberg modules
    2018/06/14 by Jakobsen, Mads S., Luef, Franz · 1 citation
    #42C15 #58B34 #FOS: Mathematics #Functional Analysis (math.FA)
17. Differential smoothness of skew polynomial rings
    2016/09/13 by Brzeziński, Tomasz, Lomp, Christian · 1 citation
    #16E45 #16S36 #16S38 #58B34 #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)
18. The C^*-algebras of quantum lens and weighted projective spaces
    2016/03/14 by Brzeziński, Tomasz, Szymański, Wojciech · 1 citation
    #46L87 #58B32 #58B34 #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA)
19. An essay on the Riemann Hypothesis
    2015/09/18 by Alain Connes, Connes, Alain · 3 voices
    Mathematics · #11S40 #14M25 #14T05 #18F10 #18F25 #58B34 #58C40 #FOS: Mathematics #Number Theory (math.NT) #Quantum Algebra (math.QA) #math.NT #math.QA
20. Smooth geometry of the noncommutative pillow, cones and lens spaces
    2014/10/24 by Brzeziński, Tomasz, Sitarz, Andrzej · 1 citation
    #58B32 #58B34 #FOS: Mathematics #Quantum Algebra (math.QA)
21. Compact quantum metric spaces from quantum groups of rapid decay
    2014/06/03 by Bhowmick, Jyotishman, Voigt, Christian, Zacharias, Joachim · 1 citation
    #58B34 #81R50 #FOS: Mathematics #Operator Algebras (math.OA) #Primary 46L87 #Quantum Algebra (math.QA) #Secondary 53C32
22. Higher rho invariants and the moduli space of positive scalar curvature metrics
    2013/10/03 by Zhizhang Xie, Xie, Zhizhang, Guoliang Yu +1 · 1 citation
    Mathematics · Physics and Astronomy · #19D55 #20F65 #46L80 #53C23 #58B34 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Group Theory (math.GR) #K-Theory and Homology (math.KT) #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA)
23. Positive scalar curvature, higher rho invariants and localization algebras
    2013/02/18 by Zhizhang Xie, Guoliang Yu, Xie, Zhizhang +1 · 2 citations
    Mathematics · Physics and Astronomy · #46L80 #53C20 #58B34 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #K-Theory and Homology (math.KT) #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA)
24. Noncommutative complex differential geometry
    2012/09/17 by Beggs, Edwin, Smith, S. Paul · 2 citations
    #14A22 #46L87 #58B32 #58B34 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Quantum Algebra (math.QA)
25. A relative higher index theorem, diffeomorphisms and positive scalar curvature
    2012/04/16 by Zhizhang Xie, Guoliang Yu, Xie, Zhizhang +1 · 3 citations
    Mathematics · #46L80 #53C20 #58B34 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)
26. Geometry of Quantum Projective Spaces
    2012/03/03 by D'Andrea, Francesco, Landi, Giovanni · 1 citation
    #20G42 #58B34 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)
27. Scalar Curvature for the Noncommutative Two Torus
    2011/10/16 by Fathizadeh, Farzad, Khalkhali, Masoud · 1 citation
    #46L87 #58B34 #Differential Geometry (math.DG) #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA)
28. Modular Curvature for Noncommutative Two-Tori
    2011/10/16 by Connes, Alain, Moscovici, Henri · 1 citation
    #46L87 #58B34 #Differential Geometry (math.DG) #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA)
29. Deformation Quantization for Actions of Kählerian Lie Groups
    2011/09/15 by Bieliavsky, Pierre, Gayral, Victor · 1 citation
    #22E30 #32M15 #46L87 #53C35 #53D55 #58B34 #81R30 #81R60 #FOS: Mathematics #Operator Algebras (math.OA)
30. The space of Penrose tilings and the non-commutative curve with homogeneous coordinate ring k/(y²)
    2011/04/19 by S. Paul Smith, Smith, S. Paul · 1 citation
    Mathematics · Physics and Astronomy · #14A22 #16E20 #16E50 #16S38 #16W50 #19K14 #52C20 #52C22 #58B34 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Rings and Algebras (math.RA)

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