Morita equivalence of smooth noncommutative tori
نویسندگان
چکیده
منابع مشابه
Morita Equivalence of Smooth Noncommutative Tori
We show that in the generic case the smooth noncommutative tori associated to two n×n real skew-symmetric matrices are Morita equivalent if and only if the matrices are in the same orbit of the natural SO(n, n|Z) action.
متن کاملMorita equivalence of multidimensional noncommutative tori
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...
متن کاملStrong Morita Equivalence of Higher-dimensional Noncommutative Tori
Let n ≥ 2 and Tn be the space of n × n real skew-symmetric matrices. For each θ ∈ Tn the corresponding n-dimensional noncommutative torus Aθ is defined as the universal C-algebra generated by unitaries U1, · · · , Un satisfying the relation UkUj = e(θkj)UjUk, where e(t) = e. Noncommutative tori are one of the canonical examples in noncommutative differential geometry [12, 2]. One may also consi...
متن کاملStrong Morita Equivalence of Higher-dimensional Noncommutative Tori. Ii
We show that two C∗-algebraic noncommutative tori are strongly Morita equivalent if and only if they have isomorphic ordered K0-groups and centers, extending N. C. Phillips’s result in the case that the algebras are simple. This is also generalized to the twisted group C∗-algebras of arbitrary finitely generated abelian groups.
متن کاملNoncommutative 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Mathematica
سال: 2007
ISSN: 0001-5962
DOI: 10.1007/s11511-007-0017-9