Results 1  10
of
16
Universal C∗algebraic quantum groups arising . . .
, 1997
"... In this paper, we construct a universal C ∗algebraic quantum group out of an algebraic one. We show that this universal C ∗algebraic quantum has the same rich structure as its reduced companion (see [9]). This universal C ∗algebraic quantum group also satisfies an upcoming definition of Masuda, N ..."
Abstract

Cited by 30 (2 self)
 Add to MetaCart
In this paper, we construct a universal C ∗algebraic quantum group out of an algebraic one. We show that this universal C ∗algebraic quantum has the same rich structure as its reduced companion (see [9]). This universal C ∗algebraic quantum group also satisfies an upcoming definition of Masuda, Nakagami & Woronowicz except for the possible nonfaithfulness of the left Haar weight.
Weight theory for C*algebraic quantum groups
, 1999
"... In this paper, we collect some technical results about weights on C∗algebras which are useful in de theory of locally compact quantum groups in the C∗algebra framework (see [17]). We discuss the extension of a lower semicontinuous weight to a normal weight following S. Baaj (see [1]), look into s ..."
Abstract

Cited by 9 (2 self)
 Add to MetaCart
In this paper, we collect some technical results about weights on C∗algebras which are useful in de theory of locally compact quantum groups in the C∗algebra framework (see [17]). We discuss the extension of a lower semicontinuous weight to a normal weight following S. Baaj (see [1]), look into slice weights and their KSGNSconstructions and investigate the tensor product of weights together with a partial GNSconstruction for such a tensor product.
KMSweights on C*algebras
, 1997
"... In this paper, we build a solid framework for the use of KMSweights on C∗algebras. We will use another definition than the one introduced by Combes in [4], but we will prove that they are equivalent. However, the subject of KMSweights is approached from a somewhat different angle. We introduce a ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
In this paper, we build a solid framework for the use of KMSweights on C∗algebras. We will use another definition than the one introduced by Combes in [4], but we will prove that they are equivalent. However, the subject of KMSweights is approached from a somewhat different angle. We introduce a construction procedure for KMSweights, prove the most important properties of them, construct the tensor product of KMSweights and construct weights which are absolutely continuous to a given weight.
QUANTUM DOUBLE CONSTRUCTION IN THE C ∗ALGEBRA SETTING OF CERTAIN HEISENBERGTYPE QUANTUM GROUPS
, 2004
"... Abstract. In this paper, we carry out the quantum double construction of the specific quantum groups we constructed earlier, namely, the “quantum Heisenberg group algebra ” (A,∆) and its dual, the “quantum Heisenberg group ” ( Â, ˆ ∆). Our approach will be by constructing a suitable multiplicative ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Abstract. In this paper, we carry out the quantum double construction of the specific quantum groups we constructed earlier, namely, the “quantum Heisenberg group algebra ” (A,∆) and its dual, the “quantum Heisenberg group ” ( Â, ˆ ∆). Our approach will be by constructing a suitable multiplicative unitary operator. In this way, we are able to retain the C ∗algebra framework, and thus able to carry out our construction within the category of locally compact quantum groups. This construction is a kind of a generalized crossed product. To establish that the quantum double we obtain is indeed a locally compact quantum group, we will also discuss the dual of the quantum double and the Haar weights on both of these double objects. Towards the end, we also include a construction of a (quasitriangular) “quantum universal Rmatrix”. Introduction. The quantum double construction, which was originally introduced by Drinfeld in the mid80’s for (finitedimensional) Hopf algebras
QUANTUM DOUBLE CONSTRUCTION IN THE C∗ALGEBRA SETTING OF CERTAIN HEISENBERGTYPE QUANTUM GROUPS
"... Abstract. We carry out the quantum double construction of the specific quantum groups we constructed earlier, namely, the “quantum Heisenberg group algebra ” (A,∆) and its dual (Â, ∆̂). Our approach is by constructing a suitable multiplicative unitary operator, retaining the C∗algebra framework of ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. We carry out the quantum double construction of the specific quantum groups we constructed earlier, namely, the “quantum Heisenberg group algebra ” (A,∆) and its dual (Â, ∆̂). Our approach is by constructing a suitable multiplicative unitary operator, retaining the C∗algebra framework of locally compact quantum groups. We also discuss the dual of the quantum double and the Haar weights on both of these double objects. Towards the end, a construction of a (quasitriangular) “quantum universal Rmatrix ” is given.