The Standard Model in noncommutative geometry and Morita equivalence
نویسندگان
چکیده
منابع مشابه
Noncommutative fermions and Morita equivalence
We study the Morita equivalence for fermion theories on noncommutative two-tori. For rational values of the θ parameter (in appropriate units) we show the equivalence between an abelian noncommutative fermion theory and a nonabelian theory of twisted fermions on ordinary space. We study the chiral anomaly and compute the determinant of the Dirac operator in the dual theories showing that the Mo...
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One can describe an n-dimensional noncommutative torus by means of an antisymmetric n×n matrix θ. We construct an action of the group SO(n, n|Z) on the space of n× n antisymmetric matrices and show that, generically, matrices belonging to the same orbit of this group give Morita equivalent tori. Some applications to physics are sketched. By definition [R5], an n-dimensional noncommutative torus...
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We study the notion of Morita equivalence in various categories. We start with Morita equivalence and Morita duality in pure algebra. Then we consider strong Morita equivalence for C-algebras and Morita equivalence for W-algebras. Finally, we look at the corresponding notions for groupoids (with structure) and Poisson manifolds.
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ژورنال
عنوان ژورنال: Journal of Noncommutative Geometry
سال: 2016
ISSN: 1661-6952
DOI: 10.4171/jncg/242