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Furstenberg transformations on irrational rotation algebras
, 2004
"... We introduce a general class of automorphisms of rotation algebras, the noncommutative Furstenberg transformations. We prove that fully irrational noncommutative Furstenberg transformations have the tracial Rokhlin property, which is a strong form of outerness. We conclude that crossed products by ..."
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Cited by 17 (8 self)
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We introduce a general class of automorphisms of rotation algebras, the noncommutative Furstenberg transformations. We prove that fully irrational noncommutative Furstenberg transformations have the tracial Rokhlin property, which is a strong form of outerness. We conclude that crossed products
MORITA EQUIVALENT SUBALGEBRAS OF IRRATIONAL ROTATION ALGEBRAS AND REAL QUADRATIC FIELDS
, 802
"... Abstract. In this paper, we determine the isomorphic classes of Morita equivalent subalgebras of irrational rotation algebras. It is based on the solution of the quadratic Diophantine equations. We determine the irrational rotation algebras that have locally trivial inclusions. We compute the index ..."
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Abstract. In this paper, we determine the isomorphic classes of Morita equivalent subalgebras of irrational rotation algebras. It is based on the solution of the quadratic Diophantine equations. We determine the irrational rotation algebras that have locally trivial inclusions. We compute the index
AF embeddings and the numerical computation of spectra in irrational rotation algebras, preprint
"... Abstract. The spectral analysis of discretized onedimensional Schrödinger operators is a very difficult problem which has been studied by numerous mathematicians. A natural problem at the interface of numerical analysis and operator theory is that of finding finite dimensional matrices whose eigenv ..."
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Cited by 3 (1 self)
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eigenvalues approximate the spectrum of an infinite dimensional operator. In this note we observe that the seminal work of PimsnerVoiculescu on AF embeddings of irrational rotation algebras provides a nice answer to the finite dimensional spectral approximation problem for a broad class of operators
A nonspectral dense Banach subalgebra of the irrational rotation algebra
 Proc. Symp. Pure Math.,120(3):811813
, 1994
"... We give an example of a dense, simple, unital Banach subalgebra A of the irrational rotation C*algebra B, such that A is not a spectral subalgebra of B. This answers a question posed in T.W. Palmer’s paper [1]. If A is a subalgebra of an algebra B (both algebras over the complex numbers), we say th ..."
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Cited by 2 (0 self)
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We give an example of a dense, simple, unital Banach subalgebra A of the irrational rotation C*algebra B, such that A is not a spectral subalgebra of B. This answers a question posed in T.W. Palmer’s paper [1]. If A is a subalgebra of an algebra B (both algebras over the complex numbers), we say
Hopfish structure and modules over irrational rotation algebras.” Contemporary Mathematics (2006): preprint arXiv:math.QA/0604405
"... Abstract. Inspired by the group structure on S 1 /Z, we introduce a weak hopfish structure on an irrational rotation algebra A of finite Fourier series. We consider a class of simple Amodules defined by invertible elements, and we compute the tensor product between these modules defined by the hopf ..."
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Cited by 7 (3 self)
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Abstract. Inspired by the group structure on S 1 /Z, we introduce a weak hopfish structure on an irrational rotation algebra A of finite Fourier series. We consider a class of simple Amodules defined by invertible elements, and we compute the tensor product between these modules defined
The structure of crossed products of irrational rotation algebras by finite subgroups of SL2(Z)
, 2006
"... Let F ⊆ SL2(Z) be a finite subgroup (necessarily isomorphic to one of Z2, Z3, Z4, or Z6), and let F act on the irrational rotational algebra Aθ via the restriction of the canonical action of SL2(Z). Then the crossed product Aθ ⋊α F and the fixed point algebra AF θ are AF algebras. The same is true ..."
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Cited by 33 (12 self)
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Let F ⊆ SL2(Z) be a finite subgroup (necessarily isomorphic to one of Z2, Z3, Z4, or Z6), and let F act on the irrational rotational algebra Aθ via the restriction of the canonical action of SL2(Z). Then the crossed product Aθ ⋊α F and the fixed point algebra AF θ are AF algebras. The same
Homological Algebra of Mirror Symmetry
 in Proceedings of the International Congress of Mathematicians
, 1994
"... Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual Ca ..."
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Cited by 529 (3 self)
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Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual
Results 1  10
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160,867