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【期刊论文】Weak Hopf Algebras and Singular Solutions of Quantum Yang-Baxter Equation
李方, Fang Li, , ★, Steven Duplij
Commun. Math. Phys. 225, 191-217 (2002),-0001,():
-1年11月30日
We investigate a generalization of Hopf algebra slq (2) by weakening the invertibility of the generator K, i.e. exchanging its invertibility KK−1=1 to the regularity KKK=K. This leads to a weak Hopf algebra wslq (2) and a J -weak Hopf algebra vslq (2) which are studied in detail. It is shown that the monoids of group-like elements of wslq (2) and vslq (2) are regular monoids, which supports the general conjucture on the connection betweek weak Hopf algebras and regular monoids. Moreover, from wslq (2) a quasi-braided weak Hopf algebra U w q is constructed and it is shown that the corresponding quasi-R-matrix is regular RwRˆwRw =Rw.
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【期刊论文】The Right Braids, Quasi-Braided Pre-Tensor Categories, and General Yang-Baxter Operators#
李方, Fang Li*
COMMUNICATIONS IN ALGEBRA,-0001,():
-1年11月30日
This work is a development of braids, tensor categories and Yang-Baxter operators. According to Li [Li, F. (1998). Weak Hopf algebras and some new solution of quantum Yang-Baxter equation. J. AIgebra 208:72-100; Li, F. (2000). Solutions of Yang-Baxter equation in endomorphism semigroup and quasi-(co)braided almost bialgebras. Comm. Algebra 28 (5): 2253-2270], it can be seen as a continuation of studying (not necessarily invertible) solutions of the (quantum) Yang-Baxter equation. We firstly introduce the right braid monoids and discuss their properties. Then, we define pre-tensor categories, pre-tensor functors and quasi-braided pre-tensor categories, and investiage their characterizations. Three examples are given from respectively a weak Hopf algebra, a crossed S-set of a Clifford monoid and the (strict) right braid category. Two universalities of the (strict) right braid category are gotten in order to characterize a category of general Yang-Baxter operators and a quasi-braided pre-tensor category. In a pretensor category we build a general centre of a pre-tensor category as a generalization of a centre and show that it is a quasi-braided pre-tensor category. At the end, a categorical interpretation of the quantum quasi-double of a weak Hapf algebra is obtained under a certain condition.
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【期刊论文】On Quasi-Bicrossed Products of Weak Hopf Algebras
李方, Fang LI
Acta Mathematica Sinica, English Series April, 2004, Vol. 20, No.2, pp. 305-318,-0001,():
-1年11月30日
The aim of this paper is to study quasi-bicrossed products and a especially quantum quasi-doubles. Firstly, we construct one new kind of quasi-bicrossed products by weak Hopf algebras and then devote a brief discussion to this matter. And, we discuss the conditions for quasi-bicrossed products to possess the structure of almost weak Hopf algebras, containing the case of a special smash product. At the end, we give some properties on the quantum quasi-double, respectively on the quasi-R-isomorphism, the representation-theoretic interpretation and the regularity of the quasi-R-matrix.
Weak Hopf algebra,, Bicrossed product,, Quantum double,, R-matrix
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【期刊论文】Elementary operations and Laplace's theorem on quantum matrices
李方, Li Fang
J. Phys. A: Math. Gen. 26 (1993) 49.87-4Z97. Printcd in the UK,-0001,():
-1年11月30日
q-fundamental matrices are introduced and studied. Elementary operations on quantum matrices are discussed. The q-generalization of the classical Laplace's theorem is found, An application of the result is given.
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【期刊论文】The Regularity of Munn Rings and Semigroup Rings
李方, Li Fang
Acta Mathematica Sinica, New Series 1995, Vol. 11, No.1, pp.53-61,-0001,():
-1年11月30日
In this paper, the author studies the regularity of Munn rings and completely 0-simple semigroup rings. When either (i) R is a ring with identity and I and Λ are infinite, or (ii) R is a strong IBN and fully Dedekind-finite ring with identity and either I or Λ is finite, in Section 2, the regularity of the Munn ring M (R; I, Λ; P) is characterized; in Section 3, for a completely 0-simple semigroup S=Mo (G; I, Λ; P), the regularity of RS is characterized. Meantime, the author shows that for a locally finite monoid S and a ring R with identity, RS is a strong IBN ring if and only if R is so; RS is fully Dedekind-finite if and only if R is so.
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