Oriented quantum algebras （coalgebras） are generalizations of quasitriangular Hopf algebras （coquasitriangular Hopf algebras） and account for regular isotopy invariants of oriented 1-1 tangles, oriented knots and ...Oriented quantum algebras （coalgebras） are generalizations of quasitriangular Hopf algebras （coquasitriangular Hopf algebras） and account for regular isotopy invariants of oriented 1-1 tangles, oriented knots and links. Let （H, or, D, U） be an oriented quantum coalgebra over the field k. Then （H×H, φ, D×D, U× U） is a trivial oriented quantum coalgebra structure on the tensor product of coalgebra H with itself, where φ （a × b, c × d） = σ-（ a, c）σ （b, d）. This paper presents the oriented quantum coalgebra structure （ H×H, σ, D×D, U× U） on coalgebra H× H, where σ（ a × b, c× d） = σ ^-1 （ d1, a1 ） σ（ a2, c1 ） σ^-1 （ d2, b1 ） σ（ b2, c2 ）. So a nontrivial oriented quantum coalgebra structure is obtained and it is dual to Radford＇s results in the paper ＂On the tensor product of an oriented quantum algebra with itself＂ published in 2007. Theoretically, the results of this paper are important in constructing the invariants of oriented knots and links.展开更多
Let M be an approximately finite codimensional quasi-invariant subspace of the Fock space. This paper gives a formula to calculate the codimension of such spaces and uses this formula to study the structure of quasi-i...Let M be an approximately finite codimensional quasi-invariant subspace of the Fock space. This paper gives a formula to calculate the codimension of such spaces and uses this formula to study the structure of quasi-invariant subspaces of the Fock space. Especially, as one of applications, it is showed that the analogue of Beurling's theorem is not true for the Fock space L_a^2 in the case of n > 2.展开更多
基金The National Natural Science Foundation of China(No.10871042)
文摘Oriented quantum algebras （coalgebras） are generalizations of quasitriangular Hopf algebras （coquasitriangular Hopf algebras） and account for regular isotopy invariants of oriented 1-1 tangles, oriented knots and links. Let （H, or, D, U） be an oriented quantum coalgebra over the field k. Then （H×H, φ, D×D, U× U） is a trivial oriented quantum coalgebra structure on the tensor product of coalgebra H with itself, where φ （a × b, c × d） = σ-（ a, c）σ （b, d）. This paper presents the oriented quantum coalgebra structure （ H×H, σ, D×D, U× U） on coalgebra H× H, where σ（ a × b, c× d） = σ ^-1 （ d1, a1 ） σ（ a2, c1 ） σ^-1 （ d2, b1 ） σ（ b2, c2 ）. So a nontrivial oriented quantum coalgebra structure is obtained and it is dual to Radford＇s results in the paper ＂On the tensor product of an oriented quantum algebra with itself＂ published in 2007. Theoretically, the results of this paper are important in constructing the invariants of oriented knots and links.
文摘Let M be an approximately finite codimensional quasi-invariant subspace of the Fock space. This paper gives a formula to calculate the codimension of such spaces and uses this formula to study the structure of quasi-invariant subspaces of the Fock space. Especially, as one of applications, it is showed that the analogue of Beurling's theorem is not true for the Fock space L_a^2 in the case of n > 2.
