李方
代数表示论,Hopf代数和量子群,环与代数,群和半群的表示理论。
个性化签名
- 姓名:李方
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学术头衔:
博士生导师
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学科领域:
应用数学
- 研究兴趣:代数表示论,Hopf代数和量子群,环与代数,群和半群的表示理论。
1963年出生于浙江杭州; 1991年在兰州大学数学系获博士学位; 1991-1993年在兰州大学理论物理方向作博士后; 1993年6月被兰州大学聘为副教授;1993年10月从兰州大学调到东南大学应用数学系工作; 1996年4月被东南大学破格聘为教授; 1998年3月从东南大学调到浙江大学(原杭州大学)数学系工作;2000年3月被批准为博士生导师。先后多次到中科院研究生院、中科院数学所、南开数学所、香港城市大学、澳大利亚Tasmania大学、西澳大利亚大学、悉尼大学、Queensland大学、New South Wiles大学、德国Bielefeld大学、慕尼黑大学、英国Warwick大学等进行学术访问。多年来为德国Zentralblatt fur Math.和美国Math.Reviews两刊物评论员;是美国数学会会员、欧洲数学会会员,浙江省国际科学技术合作协会理事。已培养研究生和访问学者若干名。1996年至今主持国家自然科学基金二项,浙江省自然科学基金一项;2001年主持国家外专局项目一项,包氏出国基金一项。获1998年江苏省科技进步三等奖一项(排名二),浙江省教委科技进步三等奖一项(独立),2002年浙江省高校科研成果一等奖一项(主持),浙江省科技进步三等奖一项(主持),2001年浙江省优秀论文奖二项。获1994年度东南大学优秀青年教师奖,1998年被选为浙江省151人才工程培养对象,2000年浙江大学校级先进工作者。入选2004年国家教育部“新世纪优秀人才支持计划”人选。授课情况:(本科生) 高等代数, 近世代数, 数学分析 , 群论, 群表示论 , 环论, 矩阵论; 研究生: Hopf代数, 量子群, 代数表示论, 同调代数, 非交换代数, Lie代数 目前主要研究兴趣:代数表示论,Hopf代数和量子群,环与代数,群和半群的表示理论。已发表论文49篇。
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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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【期刊论文】Weak Hopf Algebras and Some New Solutions of the Quantum Yang-Baxter Equation*
李方, Fang Li
JOURNAL OF ALGEBRA 208, 72-100(1998),-0001,():
-1年11月30日
In this paper, the concepts of a weak Hopf algebra and a quasi-braided almost bialgebra are introduced. It is shown that the quantum quasi-doubles of some weak Hopf algebras are quasi-braided almost bialgebras. This fact implies that some new solutions of the quantum Yang-Baxter equation can be constructed from some weak Hopf algebras, in particular, when the weak Hopf algebra is a finite Clifford monoid algebra.
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李方, Fang Li, Zhongkui Liu
Acta Mathematica Sinica, English Series 2000, Jan., Vol. 16, No.1, p. 71-78,-0001,():
-1年11月30日
In this paper, a su cient condition is given under which the smash product A#H is a trans nite left free normalizing extension of an algebra A. Moreover, the result is applied to a skew semigroup ring, a skew group ring and the quantum group Uq(sl(2)) such that some properties are shown.
Smash product,, Trans nite left free normalizing extension,, Skew semigroup ring,, Quantum Group
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李方
数学学报,2000,3(45):399~414,-0001,():
-1年11月30日
本文在余代数上定义了五类等价关系,它们是Green等价g,D,L,R,H。然后给出了这些等价关系一些基本性质和结构特点。在每个Green等价的等价类集上构造了一种偏序并给出了偏序上半格和结构的刻划。用g-,L-,R-类分别出了子余代数、左余理想、右余理想的结构刻划。进一步地,本文研究了张量积上的Green等价划及余代数同态的Green保持性和提升性。作为应用,本文得到了两个不可约余代数的张量积仍为不可约余代数的一人重要条件;证明了不可约余、代数在g-保持余代数同态下的同态像是不可约的。
余代数, Green等价, 偏序, 不可约性
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