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The first cohomology group of trivial extensions of special biserial algebra.

2003年

作者： Lial Margaret L.

来源：畅想之星图书光盘版（南... 评论

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畅想之星图书光盘版（南通市图书馆镜像）

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Science China Mathematics 2004年第4期47卷 578-592页

作者： XU YungeDepartment of Mathematics & Computer Sciences, Hubei University, Wuhan 430062, China Department of Mathematics & Computer Sciences Hubei University Wuhan China Institute of Mathematics Chinese Academy of Sciences Beijing China

Given a finite dimensional special biserial algebra.A with normed basis we obtain the dimension formulae of the first Hochschild homology groups of A and the vector space Alt(DA). As a consequence, an explicit dimension formula of the first Hochschild cohomology group of trivial extension TA = A × DA in terms of the combinatorics of the quiver and relations is determined.

关键词： Hochschild (co)homology, trivial extension, special biserial algebra.

Inhomogeneous Quantum Invariance Group of Multi-Dimensional Multi-parameter Deformed Boson algebra

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Chinese Physics Letters 2012年第1期29卷 8-10页

作者： Azmi Ali Altintas Metin Arik Ali Serdar Arikan Emre Dil Faculty of Engineering Okan UniversityTuzlaIstanbulTurkey Department of Physics Boğazici UniversityBebekIstanbulTurkey Department of Physics Sakarya UniversityEsentepeSakaryaTurkey

We investigate the inhomogeneous invariance quantum group of the d-dimensional d-parameter deformed boson *** is found that the homogeneous part of this quantum group is given by the𝑑-parameter deformed general linear *** construct the d-matrix which collects all information about the non-commuting structure of the quantum group for the two-dimensional case.

关键词： group. algebra. parameter

P-twisted affine Lie algebra.and its realizations by twisted vertex operators

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维普期刊数据库

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Science China Mathematics 2005年第Z1期48卷 295-305页

作者： LU Keping, CHU Yanjun, ZHENG Zhujun & DONG Wenfeng Institute of Mathematics, Henan University, Kaifeng 475001, China USTC Shanghai Institute for Advanced Studies, University of Science and Technology of China, Shanghai 201315, China Institute of Mathematics Henan University Kaifeng China USTC Shanghai Institute for Advanced Studies University of Science and Technology of China Shanghai China

In this paper, we define a P-twisted affine Lie algebra. and construct its realizations by twisted vertex operators.

关键词： P-twisted affine Lie algebra. twisted vertex operator, extended P-twisted afline algebra.

Relative local control and the block source algebra.

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Science China Mathematics 1997年第8期40卷 785-798页

作者：樊恽 Department of Mathematics Wuhan UniversityWuhan 430072China

The local control of pointed groups is generalized to the concept of relative local control,and it is proved that there exists a lifting for a covering of a block source algebra.if the relative local control *** an application,a result is proved on the source algebra. of blocks,whose defect groups are direct products of a normal subgroup and a subgroup that gives a relative local control.

关键词： finite group modular representation pointed group relative local control block source algebra.

Monomial Hopf algebra. over fields of positive characteristic

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Science China Mathematics 2006年第3期49卷 320-329页

作者： LIU Gongxiang & YE Yu Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China Department of Mathematics, University of Science and Technology of China, Hefei 230026, China Institute of Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Department of Mathematics University of Science and Technology of China Hefei China

In this paper, we study the structures of monomial Hopf algebra. over a field of positive characteristic. A necessary and sufficient condition for the monomial coalgebra.Cd(n) to admit Hopf structures is given here, and if it is the case, all graded Hopf structures on Cd(n)are completely classified. Moreover, we construct a Hopf algebra. filtration on Cd(n) which will help us to discuss a conjecture posed by Andruskiewitsch and Schneider. Finally combined with a theorem by Montgomery, we give the structure theorem for all monomial Hopf algebra..

关键词： monomial coalgebra. Gaussian binomial coefficient, monomial Hopf algebra.

Weighted composition operators and locally convex algebra.

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Science China Mathematics 2005年第Z1期48卷 32-46页

作者： Edoardo Vesentini Politecnico di Torino Dipartimento di Matematica Corso Duca degli Abruzzi 2410129 TorinoItaly

The Gleason-Kahane-Zelazko theorem characterizes the continuous homomorphism of an associative, locally multiplicatively convex, sequentially complete algebra.A into the field C among all linear forms on A. This characterization will be applied along two different directions. In the case in which A is a commutative Banach algebra. the theorem yields the representation of some classes of continuous linear maps A: A → A as weighted composition operators, or as composition operators when A is a continuous algebra.endomorphism. The theorem will then be applied to explore the behaviour of continuous linear forms on quasi-regular elements, when A is either the algebra.of all Hilbert-Schmidt operators or a Hilbert algebra.

关键词： linear isometry, character, Banach algebra. locally multiplicatively convex algebra.

Theoretical study of nonlinear triatomic molecular potential energy surfaces:Lie algebra.c method

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Science China Chemistry 2000年第3期43卷 247-252页

作者：郑雨军丁世良 Institute of Theoretical Chemistry Shandong University Jinan 250100 China

Triatomic molecular potential energy surfaces (PES) are obtained by using coherent state to take the classical limits of algebra.c Hamiltonian. The algebra.c Hamiltonian for bent tria-tomic molecules can be obtained using Lie algebra.c method (the expansion coefficients are obtained by fitting spectroscopic data). This PES is applied to H2O molecule, and good results are obtained.

关键词： triatomic molecule potential energy surface highly excited vibrational states Lie algebra.

On Wiener type Banach algebra

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Science China Mathematics 2003年第2期46卷 207-214页

作者：胡俊云李晓培孙顺华徐宪民 Institute of Mathematics Jiaxing University Department of Mathematics Sichuan University Department of Basic Sciences Zhanjiang Ocean University Zhanjiang 524025 China Department of Mathematics Sichuan University Chengdu 610064 China

A clarified study on the G-complete symmetry Banach algebra.is given. A Wiener type Banach algebra.as well as its stucture is introduced and studied. An application of this algebra.is presented.

关键词： G-complete symmetry Banach algebra. commutative Banach algebra. Wiener typeBanach algebra.

Minimal Representations of Cuntz algebra.

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Acta Mathematica Sinica,English Series 2020年第7期36卷 749-764页

作者： Ling Juan YE Li Ning JIANG School of Mathematics and Statistics Beijing Institute of TechnologyBeijing 100081P.R.China

Suppose that O_n(2 ≤ n ≤∞) is a Cuntz algebra. There exists a number 1 ≤ k(π, Ω) ≤∞such that if the cyclic representations(H, π, Ω) and(H, π, Ω) of the Cuntz algebra.O_n are unitary equivalent, k(π, Ω) = k(π, Ω). Applying the number, one can define a minimal representation of O_n and give a sufficient condition of the minimality for a representation of O_n. Moreover, the relations between minimal states and minimal representations of Cuntz algebra. and the relations between the minimality and the irreducibility of the representation of O_n are investigated, respectively.

关键词： algebra. O_n representation