Noncommutative space | Wikipedia audio article
Channel: wikipedia tts
Date: 30/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Noncommutative_geometry


00:00:52 1 Motivation
00:03:23 1.1 Applications in mathematical physics
00:03:51 1.2 Motivation from ergodic theory
00:04:22 2 Noncommutative C*-algebras, von Neumann algebras
00:05:10 3 Noncommutative differentiable manifolds
00:06:36 4 Noncommutative affine and projective schemes
00:08:25 5 Invariants for noncommutative spaces
00:09:35 6 Examples of noncommutative spaces
00:10:41 7 See also



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SUMMARY
=======
Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces that are locally presented by noncommutative algebras of functions (possibly in some generalized sense). A noncommutative algebra is an associative algebra in which the multiplication is not commutative, that is, for which 
  
    
      
        x
        y
      
    
    {\displaystyle xy}
   does not always equal 
  
    
      
        y
        x
      
    
    {\displaystyle yx}
  ; or more generally an algebraic structure in which one of the principal binary operations is not commutative; one also allows additional structures, e.g. topology or norm, to be possibly carried by the noncommutative algebra of functions.