Results 11  20
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49
Integral noncommutative spaces
 J. Algebra
"... Abstract. This paper concerns the closed points, closed subspaces, open subspaces, weakly closed and weakly open subspaces, and effective divisors, on a noncommutative space. 1. ..."
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Cited by 8 (1 self)
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Abstract. This paper concerns the closed points, closed subspaces, open subspaces, weakly closed and weakly open subspaces, and effective divisors, on a noncommutative space. 1.
Braided doubles and rational Cherednik algebras
 Adv. Math
"... Abstract. We introduce and study a large class of algebras with triangular decomposition which we call braided doubles. Braided doubles provide a unifying framework for classical and quantum universal enveloping algebras and rational Cherednik algebras. We classify braided doubles in terms of quasi ..."
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Cited by 7 (3 self)
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Abstract. We introduce and study a large class of algebras with triangular decomposition which we call braided doubles. Braided doubles provide a unifying framework for classical and quantum universal enveloping algebras and rational Cherednik algebras. We classify braided doubles in terms of quasiYetterDrinfeld (QYD) modules over Hopf algebras which turn out to be a generalisation of the ordinary YetterDrinfeld modules. To each braiding (a solution to the braid equation) we associate a QYDmodule and the corresponding braided Heisenberg double — this is a quantum deformation of the Weyl algebra where the role of polynomial algebras is played by NicholsWoronowicz algebras. Our main result is that any rational Cherednik algebra canonically embeds into the braided Heisenberg double attached to the corresponding complex reflection group.
Infinite Comatrix Corings
, 2004
"... We characterize the corings whose category of comodules has a generating set of small projective comodules in terms of the (non commutative) descent theory. In order to extricate the structure of these corings, we give a generalization of the notions of comatrix coring and Galois comodule which avoi ..."
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Cited by 6 (1 self)
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We characterize the corings whose category of comodules has a generating set of small projective comodules in terms of the (non commutative) descent theory. In order to extricate the structure of these corings, we give a generalization of the notions of comatrix coring and Galois comodule which avoid finiteness conditions. A sufficient condition for a coring to be isomorphic to an infinite comatrix coring is found. We deduce in particular that any coalgebra over a field and the coring associated to a groupgraded ring are isomorphic to adequate infinite comatrix corings. We also characterize when the free module canonically associated to a (not necessarily finite) set of group like elements is Galois.
Constructing the extended Haagerup planar algebra
, 2009
"... We construct a subfactor planar algebra, and as a corollary a subfactor, with the ‘extended Haagerup´ principal graph pair. This is the last open case from Haagerup’s 1993 list of potential principal graphs of subfactors with index in the range (4, 3 + √ 3). We prove that the subfactor planar algeb ..."
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Cited by 5 (2 self)
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We construct a subfactor planar algebra, and as a corollary a subfactor, with the ‘extended Haagerup´ principal graph pair. This is the last open case from Haagerup’s 1993 list of potential principal graphs of subfactors with index in the range (4, 3 + √ 3). We prove that the subfactor planar algebra with these principal graphs is unique. We give a skein theoretic description, and a description as a subalgebra generated by a certain element in the graph planar algebra of its principal graph. We give an explicit algorithm for evaluating closed diagrams using the skein theoretic description. This evaluation algorithm is unusual because intermediate steps may increase the number of generators in a diagram.
Graded extensions of monoidal categories
 J. ALGEBRA
, 2001
"... The longknown results of SchreierEilenbergMac Lane on group extensions are raised to a categorical level, for the classification and construction of the manifold of all graded monoidal categories, the type being given group � with 1component a given monoidal category. Explicit application is mad ..."
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Cited by 4 (3 self)
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The longknown results of SchreierEilenbergMac Lane on group extensions are raised to a categorical level, for the classification and construction of the manifold of all graded monoidal categories, the type being given group � with 1component a given monoidal category. Explicit application is made to the classification of strongly graded bialgebras over commutative rings.
TANNAKAKREIN DUALITY FOR COMPACT GROUPOIDS II, FOURIER TRANSFORM
, 2003
"... Abstract. In a series of papers, we have shown that from the representationtheory of a compact groupoid one can reconstruct the groupoid using the procedure similar to the TannakaKrein duality for compact groups. In this part we study the Fourier and FourierPlancherel transforms and prove the Plan ..."
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Cited by 3 (1 self)
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Abstract. In a series of papers, we have shown that from the representationtheory of a compact groupoid one can reconstruct the groupoid using the procedure similar to the TannakaKrein duality for compact groups. In this part we study the Fourier and FourierPlancherel transforms and prove the Plancherel theorem for compact groupoids. We also study the central functions in the algebra of square integrable functions on the isotropy groups. 1. introduction In a series of papers, we have generalized the TannakaKrein duality to compact groupoids. In [A1] we studied the representationtheory of compact groupoids. In particular, we showed that irreducible representationshave finite dimensional fibres. We also proved the Schur’s lemma, GelfandRaikov theorem and PeterWeyl theorem for compact groupoids. In this part we study the Fourier and FourierPlancherel transforms on compact groupoids. In section two we develop the theory of Fourier transforms on the Banach algebra bundle L 1 (G) of a compact groupoid G. As in the group case, a parallel theory of FourierPlancherel transform on the Hilbert space bundle L 2 (G) is constructed. This provides a surjective isometric linear isomorphism from L 2 (G) to L 2 ( ˆ G), in an appropriate sense. Also the relation between ˆ G and the conjugacy groupoid G G is studied. The results of this section are effectively used in [A2] to show that the natural homomorphism from G to its Tannaka groupoid T (G) is surjective. Section three considers the inverse Fourier and FourierPlancherel transforms. In this section we prove Plancherel theorem for compact groupoids. In section four we study the class functions and central elements in the algebras of functions on fibres of G and prove a diagonal version of the Plancherel theorem. All over this paper we assume that G is compact and the Haar system on G is normalized.