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Noncommutative structures

  • D. V. Treschev
Article

Abstract

We propose a method for constructing noncommutative analogs of objects from classical calculus, differential geometry, topology, dynamical systems, etc. The standard (commutative) objects can be obtained from noncommutative ones by natural projections (a set of canonical homomorphisms). The approach is ideologically close to the noncommutative geometry of A. Connes but differs from it in technical details.

Keywords

Vector Bundle STEKLOV Institute Compatibility Condition Associative Algebra Smooth Manifold 
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References

  1. 1.
    C. Chevalley and S. Eilenberg, “Cohomology Theory of Lie Groups and Lie Algebras,” Trans. Am. Math. Soc. 63, 85–124 (1948).MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    A. Connes, Noncommutative Geometry (Academic, San Diego, CA, 1994).MATHGoogle Scholar
  3. 3.
    V. G. Kac, “Lie Superalgebras,” Adv. Math. 26, 8–96 (1977).MATHCrossRefGoogle Scholar
  4. 4.
    D. V. Treschev, “Quantum Observables: An Algebraic Aspect,” Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk 250, 226–261 (2005) [Proc. Steklov Inst. Math. 250, 211–244 (2005)].Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2007

Authors and Affiliations

  1. 1.Steklov Institute of MathematicsRussian Academy of SciencesMoscowRussia

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