Morita Equivalence of Smooth Noncommutative Tori
نویسندگان
چکیده
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.
منابع مشابه
A Survey on Morita Equivalence of Quantum Tori
This paper is a survey on the problem of classifying non-commutative tori up to Morita equivalence and will review the necessary background and discuss some results concerning this question (see [28],[29] and [22]). The concept of Morita equivalence was first introduced in operator algebras by M.Rieffel in the 1970’s, in connection with the problem of characterizing representations of locally c...
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 کاملGabor Analysis, Noncommutative Tori and Feichtinger's Algebra
We point out a connection between Gabor analysis and noncommutative analysis. Especially, the strong Morita equivalence of noncommutative tori appears as underlying setting for Gabor analysis, since the construction of equivalence bimodules for noncommutative tori has a natural formulation in the notions of Gabor analysis. As an application we show that Feichtinger’s algebra is such an equivale...
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 کاملKronecker foliation, D1-branes and Morita equivalence of Noncommutative two-tori
It is known that the physics of open strings on a D2-brane on a two-torus is realized from the viewpoint of deformation quantization in the Seiberg-Witten limit. We study its T-dual theory, i.e. D1-brane physics on two-tori. Such theory is described by Kronecker foliation. The algebra of open strings on the D1-brane is then identified with the crossed product representation of a noncommutative ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003