In this paper, via constructing special matrices, we will show that there exists a differential calculus on Uθ（2）, where θ is an irrational number. Then using the above results, we shall discuss the properties of ...In this paper, via constructing special matrices, we will show that there exists a differential calculus on Uθ（2）, where θ is an irrational number. Then using the above results, we shall discuss the properties of infinitesimal generators of corepresentations of Uθ（2）. And in the final, we shall discuss its irreducible corepresentations and give the Peter-Weyl theorem explicitly for compact quantum group Uθ（2）.展开更多
In this paper, we first prove that the θ-deformation Uθ（2） of U（2） constructed by Connes and Violette is our special case of the quantum group Uq（2） constructed in our previous paper. Then we will show that th...In this paper, we first prove that the θ-deformation Uθ（2） of U（2） constructed by Connes and Violette is our special case of the quantum group Uq（2） constructed in our previous paper. Then we will show that the set of truces on the C^＊ -algebra Uθ, θ irrational, is determined by the set of the truces on a subalgebra of Uθ.展开更多
For a non-degenerate pair of compact quantum groups, we first construct the quantum double as an algebraic compact quantum group in an algebraic framework. Then by adopting some completion procedure, we give the unive...For a non-degenerate pair of compact quantum groups, we first construct the quantum double as an algebraic compact quantum group in an algebraic framework. Then by adopting some completion procedure, we give the universal and reduced quantum double constructions in the correspondence C＊-algebraic settings, which generalize Drinfeld＇s quantum double construction and yield new C＊-algebraic compact quantum groups.展开更多
Given a C^＊-algebra A and a comultiplication Ф on A, we show that the pair （A, Ф） is a compact quantum group if and only if the associated multiplier Hopf ^＊-algebra （A, ФA） is a compact Hopf ^＊-algebra.
In this paper,we show that the corepresentation of compact group Uθ(2) on the vector space is determined by its infinitesimal generators B0,B2,A0,A1 and A2,where θ is an irrational number.We also show that B0 and B2...In this paper,we show that the corepresentation of compact group Uθ(2) on the vector space is determined by its infinitesimal generators B0,B2,A0,A1 and A2,where θ is an irrational number.We also show that B0 and B2 commute with Aj,j = 0,1,2,so B0,A0,A1 and A2 are sl(2,C) loop algebra.Then we exhibit all irreducible representations of Uθ(2),which are different from those of group U(2),and use above results to give the classification of quantum groups Uθ(2),which is analogous to that of irrational algebra Aθ.At the same time,we also give all the forms of automorphisms on quantum group Uθ(2).展开更多
A sufficient condition is given for the multiparametric Hopf algebras to be Hopf * -algebras. Then a special subclass of the * -algebra related to a Latin square is given. After being completed, its generators are all...A sufficient condition is given for the multiparametric Hopf algebras to be Hopf * -algebras. Then a special subclass of the * -algebra related to a Latin square is given. After being completed, its generators are all of norm one.展开更多
文摘In this paper, via constructing special matrices, we will show that there exists a differential calculus on Uθ（2）, where θ is an irrational number. Then using the above results, we shall discuss the properties of infinitesimal generators of corepresentations of Uθ（2）. And in the final, we shall discuss its irreducible corepresentations and give the Peter-Weyl theorem explicitly for compact quantum group Uθ（2）.
文摘In this paper, we first prove that the θ-deformation Uθ（2） of U（2） constructed by Connes and Violette is our special case of the quantum group Uq（2） constructed in our previous paper. Then we will show that the set of truces on the C^＊ -algebra Uθ, θ irrational, is determined by the set of the truces on a subalgebra of Uθ.
基金supported by the scientific research fund for young teachers of Tianjin Polytechnic University(Grant No.029960)supported by National Natural Science Foundation of China(Grant No.11171015)
文摘For a non-degenerate pair of compact quantum groups, we first construct the quantum double as an algebraic compact quantum group in an algebraic framework. Then by adopting some completion procedure, we give the universal and reduced quantum double constructions in the correspondence C＊-algebraic settings, which generalize Drinfeld＇s quantum double construction and yield new C＊-algebraic compact quantum groups.
基金Acknowledgements The authors would like to thank the referees for their many invaluable suggestions. This work was supported by the Higher School Science and Technology Development Fund Project in Tianjin （Grant No. 20031003） and the National Natural Science Foundation of China （Grant No. 11301380）.
文摘Given a C^＊-algebra A and a comultiplication Ф on A, we show that the pair （A, Ф） is a compact quantum group if and only if the associated multiplier Hopf ^＊-algebra （A, ФA） is a compact Hopf ^＊-algebra.
基金supported by National Natural Science Foundation of China (Grant No.10971011)
文摘In this paper,we show that the corepresentation of compact group Uθ(2) on the vector space is determined by its infinitesimal generators B0,B2,A0,A1 and A2,where θ is an irrational number.We also show that B0 and B2 commute with Aj,j = 0,1,2,so B0,A0,A1 and A2 are sl(2,C) loop algebra.Then we exhibit all irreducible representations of Uθ(2),which are different from those of group U(2),and use above results to give the classification of quantum groups Uθ(2),which is analogous to that of irrational algebra Aθ.At the same time,we also give all the forms of automorphisms on quantum group Uθ(2).
文摘A sufficient condition is given for the multiparametric Hopf algebras to be Hopf * -algebras. Then a special subclass of the * -algebra related to a Latin square is given. After being completed, its generators are all of norm one.
