Based on some known facts of integrable models, this paper proposes a new （2＋1）-dimensional bilinear model equation. By virtue of the formal series symmetry approach, the new model is proved to be integrable becaus...Based on some known facts of integrable models, this paper proposes a new （2＋1）-dimensional bilinear model equation. By virtue of the formal series symmetry approach, the new model is proved to be integrable because of the existence of the higher order symmetries. The Lie point symmetries of the model constitute an infinite dimensional Kac- Moody Virasoro symmetry algebra. Making use of the infinite Lie point symmetries, the possible symmetry reductions of the model are also studied展开更多
Indefinite equation is an unsolved problem in number theory. Through explo-ration, the author has been able to use a simple elementary algebraic method to solve the solutions of all three variable indefinite equations...Indefinite equation is an unsolved problem in number theory. Through explo-ration, the author has been able to use a simple elementary algebraic method to solve the solutions of all three variable indefinite equations. In this paper, we will introduce and prove the solutions of Pythagorean equation, Fermat’s the-orem, Bill equation and so on.展开更多
Let ,4 and B be unital C＊-algebras, and let J∈A,L∈B be Hermitian invertible elements. For every T∈A and S∈B, define T^＋J=J^-1T＊J and ,S^＋L=^L-1,S＊L. Then in such a way we endow the C＊-algebras A and B with i...Let ,4 and B be unital C＊-algebras, and let J∈A,L∈B be Hermitian invertible elements. For every T∈A and S∈B, define T^＋J=J^-1T＊J and ,S^＋L=^L-1,S＊L. Then in such a way we endow the C＊-algebras A and B with indefinite structures. We characterize firstly the Jordan （J, L）＋homomorphisms on C＊-algebras. As applications, we further classify the bounded linear maps Ф： A →B preserving （J, L）-unitary elements. When ,4 = B（H） and B=B（K）, where H and K are infinite dimensional and complete indefinite inner product spaces on real or complex fields, we prove that indefinite-unitary preserving bounded linear surjections are of the form T→UVTV^-1 （任意T∈B（H）） or T→UVT^＋V^-1（任意T∈B（H））, where U∈B（K） is indefinite unitary and, V ： H→ K is generalized indefinite unitary in the first form and generalized indefinite anti-unitary in the second one. Some results on indefinite orthogonality preserving additive maps are also given.展开更多
In this paper, we define a class of extended quantum enveloping algebras Uq （f（K, J）） and some new Hopf algebras, which are certain extensions of quantum enveloping algebras by a Hopf algebra H. This construction ...In this paper, we define a class of extended quantum enveloping algebras Uq （f（K, J）） and some new Hopf algebras, which are certain extensions of quantum enveloping algebras by a Hopf algebra H. This construction generalizes some well-known extensions of quantum enveloping algebras by a Hopf algebra and provides a large of new noncommutative and nonco- commutative Hopf algebras.展开更多
The purpose of this paper is to construct quotient algebras L(A)1C/I(A) of complex degenerate composition Lie algebras L(A)1C by some ideals, where L(A)1C is defined via Hall algebras of tubular algebras A, and to pro...The purpose of this paper is to construct quotient algebras L(A)1C/I(A) of complex degenerate composition Lie algebras L(A)1C by some ideals, where L(A)1C is defined via Hall algebras of tubular algebras A, and to prove that the quotient algebras L(A)1C/I(A) are isomorphic to the corresponding affine Kac-Moody algebras. Moreover, it is shown that the Lie algebra Lre(A)1C generated by A-modules with a real root coincides with the degenerate composition Lie algebra L(A)1C generated by simple A-modules.展开更多
This paper discusses discrete-time stochastic linear quadratic （LQ） problem in the infinite horizon with state and control dependent noise, where the weighting matrices in the cost function are assumed to be indefin...This paper discusses discrete-time stochastic linear quadratic （LQ） problem in the infinite horizon with state and control dependent noise, where the weighting matrices in the cost function are assumed to be indefinite. The problem gives rise to a generalized algebraic Riccati equation （GARE） that involves equality and inequality constraints. The well-posedness of the indefinite LQ problem is shown to be equivalent to the feasibility of a linear matrix inequality （LMI）. Moreover, the existence of a stabilizing solution to the GARE is equivalent to the attainability of the LQ problem. All the optimal controls are obtained in terms of the solution to the GARE. Finally, we give an LMI -based approach to solve the GARE via a semidefinite programming.展开更多
Based on the n-fold tensor product version of the generalized double-bosonization construction,we prove the Majid conjecture of the quantum Kac-Moody algebras version.Particularly,we give explicitly the double-bosoniz...Based on the n-fold tensor product version of the generalized double-bosonization construction,we prove the Majid conjecture of the quantum Kac-Moody algebras version.Particularly,we give explicitly the double-bosonization type-crossing constructions of quantum Kac-Moody algebras for affine types G(1)2,E(1)6,and Tp,q,r,and in this way,we can recover generators of quantum Kac-Moody algebras with braided groups defined by R-matrices in the related braided tensor category.This gives us a better understanding for the algebra structures themselves of the quantum Kac-Moody algebras as a certain extension of module-algebras/module-coalgebras with respect to the related quantum subalgebras of finite types inside.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos10475055 and 90503006)the Science Research Fund of Zhejiang Provincial Education Department,China(Grant No20040969)
文摘Based on some known facts of integrable models, this paper proposes a new （2＋1）-dimensional bilinear model equation. By virtue of the formal series symmetry approach, the new model is proved to be integrable because of the existence of the higher order symmetries. The Lie point symmetries of the model constitute an infinite dimensional Kac- Moody Virasoro symmetry algebra. Making use of the infinite Lie point symmetries, the possible symmetry reductions of the model are also studied
文摘Indefinite equation is an unsolved problem in number theory. Through explo-ration, the author has been able to use a simple elementary algebraic method to solve the solutions of all three variable indefinite equations. In this paper, we will introduce and prove the solutions of Pythagorean equation, Fermat’s the-orem, Bill equation and so on.
基金The NNSF (10471082) of Chinathe YSF (20031009) of Shanxi ProvinceTsinghua Basic Research Foundation
文摘Let ,4 and B be unital C＊-algebras, and let J∈A,L∈B be Hermitian invertible elements. For every T∈A and S∈B, define T^＋J=J^-1T＊J and ,S^＋L=^L-1,S＊L. Then in such a way we endow the C＊-algebras A and B with indefinite structures. We characterize firstly the Jordan （J, L）＋homomorphisms on C＊-algebras. As applications, we further classify the bounded linear maps Ф： A →B preserving （J, L）-unitary elements. When ,4 = B（H） and B=B（K）, where H and K are infinite dimensional and complete indefinite inner product spaces on real or complex fields, we prove that indefinite-unitary preserving bounded linear surjections are of the form T→UVTV^-1 （任意T∈B（H）） or T→UVT^＋V^-1（任意T∈B（H））, where U∈B（K） is indefinite unitary and, V ： H→ K is generalized indefinite unitary in the first form and generalized indefinite anti-unitary in the second one. Some results on indefinite orthogonality preserving additive maps are also given.
基金Supported by Zhejiang Provincial Natural Science Foundation of China(Y6100148,Y610027)Education Department of Zhejiang Province(201019063)National Natural Science Foundation of China(11171296)
文摘In this paper, we define a class of extended quantum enveloping algebras Uq （f（K, J）） and some new Hopf algebras, which are certain extensions of quantum enveloping algebras by a Hopf algebra H. This construction generalizes some well-known extensions of quantum enveloping algebras by a Hopf algebra and provides a large of new noncommutative and nonco- commutative Hopf algebras.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 10371101 and 10671161)
文摘The purpose of this paper is to construct quotient algebras L(A)1C/I(A) of complex degenerate composition Lie algebras L(A)1C by some ideals, where L(A)1C is defined via Hall algebras of tubular algebras A, and to prove that the quotient algebras L(A)1C/I(A) are isomorphic to the corresponding affine Kac-Moody algebras. Moreover, it is shown that the Lie algebra Lre(A)1C generated by A-modules with a real root coincides with the degenerate composition Lie algebra L(A)1C generated by simple A-modules.
基金supported by the National Natural Science Foundation of China(Nos.61174078,61170054,61402265)the Research Fund for the Taishan Scholar Project of Shandong Province of China
文摘This paper discusses discrete-time stochastic linear quadratic （LQ） problem in the infinite horizon with state and control dependent noise, where the weighting matrices in the cost function are assumed to be indefinite. The problem gives rise to a generalized algebraic Riccati equation （GARE） that involves equality and inequality constraints. The well-posedness of the indefinite LQ problem is shown to be equivalent to the feasibility of a linear matrix inequality （LMI）. Moreover, the existence of a stabilizing solution to the GARE is equivalent to the attainability of the LQ problem. All the optimal controls are obtained in terms of the solution to the GARE. Finally, we give an LMI -based approach to solve the GARE via a semidefinite programming.
基金This work was supported in part by the National Natural Science Foundation of China(Grant Nos.11801394,11771142,11871249)and the Science and Technology Commission of Shanghai Municipality(No.18dz2271000).
文摘Based on the n-fold tensor product version of the generalized double-bosonization construction,we prove the Majid conjecture of the quantum Kac-Moody algebras version.Particularly,we give explicitly the double-bosonization type-crossing constructions of quantum Kac-Moody algebras for affine types G(1)2,E(1)6,and Tp,q,r,and in this way,we can recover generators of quantum Kac-Moody algebras with braided groups defined by R-matrices in the related braided tensor category.This gives us a better understanding for the algebra structures themselves of the quantum Kac-Moody algebras as a certain extension of module-algebras/module-coalgebras with respect to the related quantum subalgebras of finite types inside.
