Analytic Hardy and BMO spaces on the quantum torus are introduced. Some basic properties of these spaces are presented. In particular, the associated H 1-BMO duality theorem is proved. Finally, we discuss some possibl...Analytic Hardy and BMO spaces on the quantum torus are introduced. Some basic properties of these spaces are presented. In particular, the associated H 1-BMO duality theorem is proved. Finally, we discuss some possible extensions of the obtained results.展开更多
The Littlewood-Paley and Marcinkiewicz＇s multiplier theorems on the quan- tum torus are established. An key ingredient of the proof is vector-valued Littlewood-Paley and noncommutative Khinchin＇s inequalities.
Based on the symmetry of the Q-deformed Kadomtsev-Petviashvili(q-KP)hierarchy,which is a q-deformation of the KP hierarchy,we construct the quantum torus symmetry of the q-KP hierarchy,which further leads to the quant...Based on the symmetry of the Q-deformed Kadomtsev-Petviashvili(q-KP)hierarchy,which is a q-deformation of the KP hierarchy,we construct the quantum torus symmetry of the q-KP hierarchy,which further leads to the quantum torus constraint of its tau function.Moreover,we generalize the system to a multi-component q-KP hierarchy that also has the well-known ghost symmetry.展开更多
In this paper, we present some modules over the rank-three quantized Weyl algebra, which are closely related to modules over some vertex algebras. The isomorphism classes among these modules are also determined.
The author first constructs a Lie algebra ∑ ：=∑（q, Wd） from rank 3 quantum torus, which is isomorphic to the core of EALAs of type Ad-1 with coordinates in quantum torus Cqd, and then gives the necessary and suff...The author first constructs a Lie algebra ∑ ：=∑（q, Wd） from rank 3 quantum torus, which is isomorphic to the core of EALAs of type Ad-1 with coordinates in quantum torus Cqd, and then gives the necessary and sufficient conditions for the highest weight modules to be quasifinite nonzero central charges are Finally the irreducible Z-graded quasifinite ∑-modules with classified.展开更多
The coordinate ring O_(q)(K^(n))of quantum affine space is the K-algebra presented by generators x_(1),...,x_(n) and relations x_(i)x_(j)=q_(ij)a_(j)a_(i) for all i,j.We construct simple O_(q)(K^(n))-modules in a more...The coordinate ring O_(q)(K^(n))of quantum affine space is the K-algebra presented by generators x_(1),...,x_(n) and relations x_(i)x_(j)=q_(ij)a_(j)a_(i) for all i,j.We construct simple O_(q)(K^(n))-modules in a more general setting where the parameters qij lie in a torsion subgroup of K^(*)and show that analogous results hold as in the uniparameter case.展开更多
In this paper we classify the irreducible integrable modules for the core of the extended affine Lie algebra of type Ad-1 coordinated by Cq with finite-dimensional weight spaces and the center acting trivially, where ...In this paper we classify the irreducible integrable modules for the core of the extended affine Lie algebra of type Ad-1 coordinated by Cq with finite-dimensional weight spaces and the center acting trivially, where Cq is the quantum torus in two variables.展开更多
文摘Analytic Hardy and BMO spaces on the quantum torus are introduced. Some basic properties of these spaces are presented. In particular, the associated H 1-BMO duality theorem is proved. Finally, we discuss some possible extensions of the obtained results.
文摘The Littlewood-Paley and Marcinkiewicz＇s multiplier theorems on the quan- tum torus are established. An key ingredient of the proof is vector-valued Littlewood-Paley and noncommutative Khinchin＇s inequalities.
基金supported by the National Natural Science Foundation of China under the grant No.11571192K.C.Wong Magna Fund in Ningbo University.
文摘Based on the symmetry of the Q-deformed Kadomtsev-Petviashvili(q-KP)hierarchy,which is a q-deformation of the KP hierarchy,we construct the quantum torus symmetry of the q-KP hierarchy,which further leads to the quantum torus constraint of its tau function.Moreover,we generalize the system to a multi-component q-KP hierarchy that also has the well-known ghost symmetry.
基金NSF Grant No.Z0511046 of Fujian and NSF Grant No.10471091 of China
文摘In this paper, we present some modules over the rank-three quantized Weyl algebra, which are closely related to modules over some vertex algebras. The isomorphism classes among these modules are also determined.
基金Project supported by the Post Doctorate Research Grant from the Ministry of Science and Technologyof China (No. 20060390526)the National Natural Science Foundation of China (No. 10601057)
文摘The author first constructs a Lie algebra ∑ ：=∑（q, Wd） from rank 3 quantum torus, which is isomorphic to the core of EALAs of type Ad-1 with coordinates in quantum torus Cqd, and then gives the necessary and sufficient conditions for the highest weight modules to be quasifinite nonzero central charges are Finally the irreducible Z-graded quasifinite ∑-modules with classified.
文摘The coordinate ring O_(q)(K^(n))of quantum affine space is the K-algebra presented by generators x_(1),...,x_(n) and relations x_(i)x_(j)=q_(ij)a_(j)a_(i) for all i,j.We construct simple O_(q)(K^(n))-modules in a more general setting where the parameters qij lie in a torsion subgroup of K^(*)and show that analogous results hold as in the uniparameter case.
基金The third author was partially supported by NSF of China （10931006） and a grant from the PhD Programs Foundation of Ministry of Education of China （20100121110014）. The fourth author was partially supported by NSF of China （11371024）, Natural Science Foundation of Fujian Province （2013J01018） and Fundamental Research Funds for the Central University （2013121001）.
文摘In this paper we classify the irreducible integrable modules for the core of the extended affine Lie algebra of type Ad-1 coordinated by Cq with finite-dimensional weight spaces and the center acting trivially, where Cq is the quantum torus in two variables.
