We present a 9×9 S-matrix and E-matrix.A representation of specialized Birman-Wenzl-Murakami algebra is obtained.Starting from the given braid group representation S-matrix,we obtain the trigonometric solution of...We present a 9×9 S-matrix and E-matrix.A representation of specialized Birman-Wenzl-Murakami algebra is obtained.Starting from the given braid group representation S-matrix,we obtain the trigonometric solution of Yang-Baxter equation.A unitary matrix R(x,φ1,φ2)is generated via the Yang-Baxterization approach.Then we construct a Yang-Baxter Hamiltonian through the unitary matrix R(x,φ1,φ2).Berry phase of this Yang-Baxter system is investigated in detail.展开更多
In this paper,we compute Rota-Baxter operators on the 3-dimensional Lie algebra g whose derived algebra’s dimension is 2.Furthermore,we give the corresponding solutions of the classical Yang-Baxter equation in the 6-...In this paper,we compute Rota-Baxter operators on the 3-dimensional Lie algebra g whose derived algebra’s dimension is 2.Furthermore,we give the corresponding solutions of the classical Yang-Baxter equation in the 6-dimensional Lie algebras g ■ _(ad~*) g~* and some new structures of left-symmetric algebra induced from g and its Rota-Baxter operators.展开更多
Constant solutions to Yang-Baxter equation are investigated over Grassmann algebra for the case of 6-vertex R-matrix. The general classification of all possible solutions over Grassmann algebra and particular cases wi...Constant solutions to Yang-Baxter equation are investigated over Grassmann algebra for the case of 6-vertex R-matrix. The general classification of all possible solutions over Grassmann algebra and particular cases with 2,3,4 generators are studied. As distinct from the standard case, when R-matrix over number field can have a maximum 5 nonvanishing elements, we obtain over Grassmann algebra a set of new full 6-vertex solutions. The solutions leading to regular R-matrices which appear in weak Hopf algebras are considered.展开更多
Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bound...Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bounded functions L<sup>∞</sup>(X, μ) on X. We confirm that the commutative von Neumann algebras M⊂B(H), with H=L<sup>2</sup>(X, μ), are unitary equivariant to the maximal ideals of the commutative algebra C(X). Subsequenly, we use the measure groupoid to formulate the algebraic and topological structures of the commutative algebra C(X) following its action on M(X) and define its representation and ergodic dynamical system on the commutative von Neumann algebras of M of B(H) .展开更多
In this paper, from the spacetime algebra associated with the Minkowski space ℝ3,1by means of a change of signature, we describe a quaternionic representation of the split-tetraquaternion algebra which incorporates th...In this paper, from the spacetime algebra associated with the Minkowski space ℝ3,1by means of a change of signature, we describe a quaternionic representation of the split-tetraquaternion algebra which incorporates the Pauli algebra, the split-biquaternion algebra and the split-quaternion algebra, we relate these algebras to Clifford algebras and we show the emergence of the stabilized Poincaré-Heisenberg algebra from the split-tetraquaternion algebra. We list without going into details some of their applications in Physics and in Born geometry.展开更多
Because homology on compact homogeneous nilpotent manifolds is closely related to homology on Lie algebras, studying homology on Lie algebras is helpful for further studying homology on compact homogeneous nilpotent m...Because homology on compact homogeneous nilpotent manifolds is closely related to homology on Lie algebras, studying homology on Lie algebras is helpful for further studying homology on compact homogeneous nilpotent manifolds. So we start with the differential sequence of Lie algebras. The Lie algebra g has the differential sequence E0,E1,⋯,Es⋯, which leads to the chain complex Es0→Δs0Ess→Δs1⋯→ΔsiEs(i+1)s→Δsi+1⋯of Esby discussing the chain complex E10→Δ10E11→Δ11⋯→Δ1r−1E1r→Δ1r⋯of E1and proves that Es+1i≅Hi(Es)=KerΔsi+1/ImΔsiand therefore Es+1≅H(Es)by the chain complex of Es(see Theorem 2).展开更多
For the Zn-symmetric statistical model the Yang-Baxter equation and the equations for the operator representations is reduced to explicit spectroparameter-independent forms,and the quantum algebra for the representati...For the Zn-symmetric statistical model the Yang-Baxter equation and the equations for the operator representations is reduced to explicit spectroparameter-independent forms,and the quantum algebra for the representations is obtained.Moreover,we present some elliptic representations of braid group,which include a new trigonometric representation as degenerated case.展开更多
The superiority of hypothetical quantum computers is not due to faster calculations but due to different scheme of calculations running on special hardware. At the same time, one should realize that quantum computers ...The superiority of hypothetical quantum computers is not due to faster calculations but due to different scheme of calculations running on special hardware. At the same time, one should realize that quantum computers would only provide dramatic speedups for a few specific problems, for example, factoring integers and breaking cryptographic codes in the conventional quantum computing approach. The core of quantum computing follows the way a state of a quantum system is defined when basic things interact with each other. In the conventional approach, it is implemented through the tensor product of qubits. In the suggested geometric algebra formalism simultaneous availability of all the results for non-measured observables is based on the definition of states as points on a three-dimensional sphere, which is very different from the usual Hilbert space scheme.展开更多
In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better...In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.展开更多
基金Supported by National Natural Science Foundation of China under Grants No.10875026
文摘We present a 9×9 S-matrix and E-matrix.A representation of specialized Birman-Wenzl-Murakami algebra is obtained.Starting from the given braid group representation S-matrix,we obtain the trigonometric solution of Yang-Baxter equation.A unitary matrix R(x,φ1,φ2)is generated via the Yang-Baxterization approach.Then we construct a Yang-Baxter Hamiltonian through the unitary matrix R(x,φ1,φ2).Berry phase of this Yang-Baxter system is investigated in detail.
基金The NSF(11047030 and 11771122) of Chinathe Science and Technology Program(152300410061) of Henan Province
文摘In this paper,we compute Rota-Baxter operators on the 3-dimensional Lie algebra g whose derived algebra’s dimension is 2.Furthermore,we give the corresponding solutions of the classical Yang-Baxter equation in the 6-dimensional Lie algebras g ■ _(ad~*) g~* and some new structures of left-symmetric algebra induced from g and its Rota-Baxter operators.
文摘Constant solutions to Yang-Baxter equation are investigated over Grassmann algebra for the case of 6-vertex R-matrix. The general classification of all possible solutions over Grassmann algebra and particular cases with 2,3,4 generators are studied. As distinct from the standard case, when R-matrix over number field can have a maximum 5 nonvanishing elements, we obtain over Grassmann algebra a set of new full 6-vertex solutions. The solutions leading to regular R-matrices which appear in weak Hopf algebras are considered.
文摘Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bounded functions L<sup>∞</sup>(X, μ) on X. We confirm that the commutative von Neumann algebras M⊂B(H), with H=L<sup>2</sup>(X, μ), are unitary equivariant to the maximal ideals of the commutative algebra C(X). Subsequenly, we use the measure groupoid to formulate the algebraic and topological structures of the commutative algebra C(X) following its action on M(X) and define its representation and ergodic dynamical system on the commutative von Neumann algebras of M of B(H) .
文摘In this paper, from the spacetime algebra associated with the Minkowski space ℝ3,1by means of a change of signature, we describe a quaternionic representation of the split-tetraquaternion algebra which incorporates the Pauli algebra, the split-biquaternion algebra and the split-quaternion algebra, we relate these algebras to Clifford algebras and we show the emergence of the stabilized Poincaré-Heisenberg algebra from the split-tetraquaternion algebra. We list without going into details some of their applications in Physics and in Born geometry.
文摘Because homology on compact homogeneous nilpotent manifolds is closely related to homology on Lie algebras, studying homology on Lie algebras is helpful for further studying homology on compact homogeneous nilpotent manifolds. So we start with the differential sequence of Lie algebras. The Lie algebra g has the differential sequence E0,E1,⋯,Es⋯, which leads to the chain complex Es0→Δs0Ess→Δs1⋯→ΔsiEs(i+1)s→Δsi+1⋯of Esby discussing the chain complex E10→Δ10E11→Δ11⋯→Δ1r−1E1r→Δ1r⋯of E1and proves that Es+1i≅Hi(Es)=KerΔsi+1/ImΔsiand therefore Es+1≅H(Es)by the chain complex of Es(see Theorem 2).
文摘For the Zn-symmetric statistical model the Yang-Baxter equation and the equations for the operator representations is reduced to explicit spectroparameter-independent forms,and the quantum algebra for the representations is obtained.Moreover,we present some elliptic representations of braid group,which include a new trigonometric representation as degenerated case.
文摘The superiority of hypothetical quantum computers is not due to faster calculations but due to different scheme of calculations running on special hardware. At the same time, one should realize that quantum computers would only provide dramatic speedups for a few specific problems, for example, factoring integers and breaking cryptographic codes in the conventional quantum computing approach. The core of quantum computing follows the way a state of a quantum system is defined when basic things interact with each other. In the conventional approach, it is implemented through the tensor product of qubits. In the suggested geometric algebra formalism simultaneous availability of all the results for non-measured observables is based on the definition of states as points on a three-dimensional sphere, which is very different from the usual Hilbert space scheme.
基金partially supported by the Natural Sciences and Engineering Research Council of Canada(2019-03907)。
文摘In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.
基金Supported by Educational Ministry Key Foundation of China(108154)Na- tional Natural Science Foundation of China(10871170)Young Teachers of College of Science,Nanjing Agricultural University(LXY20090101)
