The aim of this paper is to outline the conditions of a conformal hyperquaternion algebra H<sup>⊗2m</sup> in which a higher order plane curve can be described by generalizing the well-known cases of conics...The aim of this paper is to outline the conditions of a conformal hyperquaternion algebra H<sup>⊗2m</sup> in which a higher order plane curve can be described by generalizing the well-known cases of conics and cubic curves in 2D. In other words, the determination of the order of a plane curve through n points and its conformal hyperquaternion algebra H<sup>⊗2m</sup> is the object of this work.展开更多
The embedding theorem ofZ-graded Lie superalgebras is given and proved. As a subsidiary result it is proved that a transitiveZ-graded restricted lie superalgebm $G = \mathop \oplus \limits_{i \geqslant - 1} G_i $ must...The embedding theorem ofZ-graded Lie superalgebras is given and proved. As a subsidiary result it is proved that a transitiveZ-graded restricted lie superalgebm $G = \mathop \oplus \limits_{i \geqslant - 1} G_i $ must be isomorphic toW(m,n, 1) if the dimension ofG i satisfies a certain condition.展开更多
Let X be a connected finite CW complex and d_x: K_O(C(X))→ Z be the dimension function. We show that, if A is a unital separable simple nuclear C~*-algebra of TR(A)= 0 with the unique tracial state and satisfying the...Let X be a connected finite CW complex and d_x: K_O(C(X))→ Z be the dimension function. We show that, if A is a unital separable simple nuclear C~*-algebra of TR(A)= 0 with the unique tracial state and satisfying the UCT such that K_O (A)= Q kerd_x and K_1 (A)=K_1 (C(X)). then A is isomorphic to an inductive limit of M_n! (C(X)).展开更多
We compute the derivations of the positive part of the two-parameter quantum group Ur,s（B3） and show that the Hochschild cohomology group of degree 1 of this algebra is a three- dimensional vector space over the bas...We compute the derivations of the positive part of the two-parameter quantum group Ur,s（B3） and show that the Hochschild cohomology group of degree 1 of this algebra is a three- dimensional vector space over the base field C. We also compute the groups of （Hopf） algebra automorphisms of the augmented two-parameter quantized enveloping algebra Ur,s（B3）.展开更多
文摘The aim of this paper is to outline the conditions of a conformal hyperquaternion algebra H<sup>⊗2m</sup> in which a higher order plane curve can be described by generalizing the well-known cases of conics and cubic curves in 2D. In other words, the determination of the order of a plane curve through n points and its conformal hyperquaternion algebra H<sup>⊗2m</sup> is the object of this work.
文摘The embedding theorem ofZ-graded Lie superalgebras is given and proved. As a subsidiary result it is proved that a transitiveZ-graded restricted lie superalgebm $G = \mathop \oplus \limits_{i \geqslant - 1} G_i $ must be isomorphic toW(m,n, 1) if the dimension ofG i satisfies a certain condition.
基金Research partially supported by NSF Grants DMS 9801482
文摘Let X be a connected finite CW complex and d_x: K_O(C(X))→ Z be the dimension function. We show that, if A is a unital separable simple nuclear C~*-algebra of TR(A)= 0 with the unique tracial state and satisfying the UCT such that K_O (A)= Q kerd_x and K_1 (A)=K_1 (C(X)). then A is isomorphic to an inductive limit of M_n! (C(X)).
基金supported by Specialized Research Fund for the Doctoral Program of Highter Education(Grant No.20130031110005)supported by NSFC(Grant No.11271131)
文摘We compute the derivations of the positive part of the two-parameter quantum group Ur,s（B3） and show that the Hochschild cohomology group of degree 1 of this algebra is a three- dimensional vector space over the base field C. We also compute the groups of （Hopf） algebra automorphisms of the augmented two-parameter quantized enveloping algebra Ur,s（B3）.
