The counterpart of simple AF C*-algebras in the von Neumann algebra world are the hyperfinite factors, which were classified by Connes and Haagerup.
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Connes obtained the analogous result for the II∞ factor.
In von Neumann algebras, the Connes embedding problem or conjecture, due to Alain Connes, asks whether every free ultrafilter.
Dirk Kreimer (born 1960) is a German physicist who pioneered the Hopf-algebraic approach to quantum field theory with Alain Connes and other co-authors.
Noncommutative geometry, quantum fields and motives. (with Alain Connes), American Mathematical Society, Colloquium Publications, 2008.
Many topological and geometric properties of the classical 2-torus have algebraic analogues for the noncommutative tori, and as such they are fundamental examples of a noncommutative space in the sense of Alain Connes.
A possible solution to this problem has been put forward by Carlo Rovelli and Alain Connes, both in the classical and quantum theory, and goes by the name of the thermal time hypothesis.
His work on knot polynomials, with the discovery of what is now called the Jones polynomial, was from an unexpected direction with origins in the theory of von Neumann algebras, an area of analysis already much developed by Alain Connes.
Alain Delon | Alain Bashung | Alain Resnais | Alain Prost | Alain Whyte | Alain Touraine | Alain Connes | Alain Badiou | Alain Souchon | Alain Chamfort | Alain Juppé | Jehan Alain | Alain Rohr | Alain Ducasse | Alain Veinstein | Alain Tanner | Alain Robert | Alain-Fournier | Alain Bosquet | Jacques-Alain Miller | Alain Lombard | Alain de Mijolla | Alain de Botton | Alain de Benoist | Alain Daniélou | Alain Clark | Alain Barrière | Alain Afflelou | Alain Sailhac | Alain-René Lesage |