Noncommutative geometry and reality
نویسنده
چکیده
We introduce the notion of real structure in our spectral geometry. This notion is motivated by Atiyah’s KR-theory and by Tomita’s involution J. It allows us to remove two unpleasant features of the “Connes-Lott” description of the standard model, namely, the use of bivector potentials and the asymmetry in the Poincare duality and in the unimodularity condition.
منابع مشابه
Algebraic Noncommutative Geometry
A noncommutative algebra A, called an algebraic noncommutative geometry, is defined, with a parameter ε in the centre. When ε is set to zero, the commutative algebra A0 of algebraic functions on an algebraic manifold M is obtained. This A0 is a subalgebra of Cω(M), which is dense if M is compact. The generators of A define an immersion of M into Rn, and M inherits a Poisson structure as the lim...
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Noncommutative geometry is based on an idea that an associative algebra can be regarded as " an algebra of functions on a noncommutative space ". The major contribution to noncommutative geometry was made by A. Connes, who, in particular, analyzed Yang-Mills theories on noncommutative spaces, using important notions that were introduced in his papers (connection, Chern character, etc). It was f...
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