摘要:

In [22], a class of four-dimensional, quadratic, Artin-Schelter regular algebras was introduced, whose point scheme is the graph of an automorphism of a nonsingular quadric in P3. These algebras are the first examples of quadratic Artin-Schelter regular algebras whose defining relations are not determined by the point scheme and, hence, not determined by the algebraic data obtained from the point modules. In this paper, we study these algebras via their line modules. In particular, the set of lines in P3that correspond to left line modules is not the set of lines in P3that correspond to right line modules. Our analysis focuses on a distinguished memberRλof this class of algebras, whereRλis a twist by a twisting system of the other algebras. We prove thatRλis a finite module over its center and that its central Proj is a smooth quadric inP4.

ISSN:0092-7872    

DOI:10.1080/00927870008826955

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008826956

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

The aim of this paper is to study the solutions of the Yang-Baxter equation in the endomorphism semigroup of the tensor product of a vector space. As preparation, we introduce the concepts of quasi-braided almost bialgebra (see also [10]) and quasi-cobraided almost bialgebra, and discuss some of their properties. In particular, it is shown that the quasi R-matrixRof every quasi-braided almost weak Hopf algebra is regular under von Neumann's meaning. The solutions of the Yang-Baxter equation in the endomorphism semigroups are constructed respectively from every quasi-braided almost bialgebra and every quasi-cobraided almost bialgebra. As examples, we explain how to build solutions of the Yang-Baxter equation from some weak Hopf algebras and all Clifford monoids. Finally, the FRT construction is given so as to build every solution of the Yang-Baxter equation from a quasi-cobraided bialgebra.

ISSN:0092-7872    

DOI:10.1080/00927870008826957

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008826958

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008826959

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

A polynomial in n variables is called a coordinate polynomial if it is a component of a polynomial automorphism ofn-space. Forn=2 and a ground field of characteristic zero, we show that a polynomial is a coordinate polynomial if its composition with a dominant endomorphism of 2-space is a coordinate polynomial.

ISSN:0092-7872    

DOI:10.1080/00927870008826960

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

LetHbe a Hopf algebra in a rigid symmetric monoidal categoryCthen the evaluation map τis a convolution-invertible skew pairing. In the previous paper, we constructed a Hopf algebraD(H)=H⋈rH*copinC. In this paper, we first show thatD(H) is a quasitriangular Hopf algebra inC. Next, letHbe an ordinary triangular finite-dimensional Hopf algebra. Then one can form quasitriangular Hopf algebrasB(H,H)andB(H,D(H))(in a rigid braided monoidal category) by Majid’s method associated to the ordinary Hopf algebra mapsH→HandiHH→D(H), whereD(H)is the Drin-fePd quantum double. We show thatD(B(H,H))andB(H,D(H))are isomorphic Hopf algebras in the braided monoidal category.

ISSN:0092-7872    

DOI:10.1080/00927870008826961

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

A prime idealpof a commutative ringRis said to be a Goldman ideal (or aG-ideal) if there exists a maximal idealMof the polynomial ringR[X] such thatp=M∩R. A topological space is said to be goldspectral if it is homeomorphic to the space Gold(R) ofG-ideals ofR(Gold(R) is considered as a subspace of the prime spectrum Spec(R) equipped with the Zariski topology). We give here a topological characterization of goldspectral spaces.

ISSN:0092-7872    

DOI:10.1080/00927870008826962

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

We give an example of an LO-pair (R,T) with dimR=dimT=n, so that all maximal ideals ofRhave the same heightn, but withTnot integral overR. This answers an open question of DavidE. Dobbs.

ISSN:0092-7872    

DOI:10.1080/00927870008826963

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor

摘要:

A prime ideal P of a ring A is said to be a strongly prime ideal if aP and bA are comparable for all a,b ϵ A. We shall say that a ring A is a pseudo-valuation ring (PVR) if each prime ideal of A is a strongly prime ideal. We show that if A is a PVR with maximal ideal M, then every overring of A is a PVR if and only if M is a maximal ideal of every overring of M that does not contain the reciprocal’of any element of M.We show that if R is an atomic domain and a PVD, then dim(R) ≤ 1. We show that if R is a PVD and a prime ideal of R is finitely generated, then every overring of R is a PVD. We give a characterization of an atomic PVD in terms of the concept of half-factorial domain.

ISSN:0092-7872    

DOI:10.1080/00927870008826964

出版商:Gordon and Breach Science Publishers Ltd.    

年代:2000

数据来源: Taylor