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Orthogonal graphs of characteristic 2 and their automorphisms

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Science China Mathematics 2009年第2期52卷 361-380页

作者： WAN ZheXian ZHOU Kai Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China

The (singular) orthogonal graph O(2ν + δ,q) over a field with q elements and of characteristic 2 (where ν 1, and δ = 0,1 or 2) is introduced. When ν = 1, O(2 · 1,q), O(2 · 1 + 1,q) and O(2 · 1 + 2,q) are complete graphs with 2, q + 1 and q2 + 1 vertices, respectively. When ν 2, O(2ν + δ,q) is strongly regular and its parameters are computed. O(2ν + 1,q) is isomorphic to the symplectic graph Sp(2ν,q). The chromatic number of O(2ν + δ,q) except when δ = 0 and ν is odd is computed and the group of graph automorphisms of O(2ν + δ,q) is determined.

关键词： singular orthogonal graphs regularity chromatic number automorphisms

Boolean automorphisms of a Hypercube Coincide with the Linear Isometries

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Advances in Pure Mathematics 2014年第8期4卷 368-372页

作者： Eberto R. Morgado Marco V. José Facultad de Matemática Física y Computación Universidad Central “Marta Abreu” de Las Villas Santa Clara Cuba Theoretical Biology Group Instituto de Investigaciones Biomédicas Universidad Nacional Autónoma de México México D.F. México

Boolean homomorphisms of a hypercube, which correspond to the morphisms in the category of finite Boolean algebras, coincide with the linear isometries of the category of finite binary metric vector spaces.

关键词： Boolean automorphisms Boolean Algebra Hypercube Linear Isometries

Determining Sets and Determining Numbers of Finite Groups

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Algebra Colloquium 2024年第1期31卷 111-128页

作者： Dengyin Wang Chi Zhang Haipeng Qu School of Mathematics China University of Mining and Technology XuzhouJiangsu 221116China School of Mathematics and Computer Science Shanxi Normal University LinfenShanxi 041000China

A subset D of a group G is a determining set of G if every automorphism of G is uniquely determined by its action on D,and the determining number of G,a(G),is the cardinality of a smallest determining set.A group G is called a DEG-group if α(G)equals(G),the generating number of *** main results are as *** groups with determining number 0 or 1 are classified;finite simple groups and finite nilpotent groups are proved to be DEG-groups;for a given finite group H,there is a DEG-group G such that H is isomorphic to a normal subgroup of G and there is an injective mapping from the set of all finite groups to the set of finite DEG-groups;for any integer k≥2,there exists a group G such that α(G)=2 and(G)≥k.

关键词： determining number automorphisms nilpotent groups

Classification of Proper Holomorphic Mappings between Hartogs Domains over Homogeneous Siegel Domains

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Acta Mathematica Sinica,English Series 2023年第11期39卷 2259-2274页

作者： Lei WANG School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074P.R.China

The Hartogs domain over homogeneous Siegel domain D_(N,s)(s>0)is defined by the inequality■,where D is a homogeneous Siegel domain of typeⅡ,(z,ζ)∈D×C~N and KD(z,z)is the Bergman kernel of ***,Seo obtained the rigidity result that proper holomorphic mappings between two equidimensional domains D_(N,s)and D'_(N',s')are biholomorphisms for N≥*** this article,we find a counter-example to show that the rigidity result is not true for D_(1,s)and obtain a classification of proper holomorphic mappings between D_(1,s)and D'_(1,s').

关键词： Hartogs domains homogeneous Siegel domain of typeⅡ proper holomorphic mappings automorphisms

New classes of test polynomials of polynomial algebras

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Science China Mathematics 1999年第7期42卷 712-719页

作者：冯克勤余解台 Graduate School at Beijing University of Science and Technology of China Beijing China Department of Mathematics University of Hong Kong Hong Kong China

A polynomial p in a polynomial algebra over a field is called a test polynomial if any endomorphism of the polynomial algebra that fixes p is an automorphism. some classes of new test polynomials recognizing nonlinear automorphisms of polynomial algebras are given. In the odd prime characteristic case, test polynomials recognizing non-semisimple automorphisms are also constructed.

关键词： test polynomials polynomial algebras endomorphisms automorphisms semisimple automorphisms.

Graded Lie Algebras of Dimension Five and Some Artin-Schelter Regular Algebras

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Algebra Colloquium 2019年第2期26卷 243-258页

作者： Yuan Shen Department of Mathematics Zhejiang Sci-Tech University Hangzhou 310018 China

In this paper, we show that there are only seven graded Lie algebras of dimension 5 generated in degree 1 up to isomorphism. By parameterizing the relations of the universal enveloping algebras of three of those graded Lie algebras, we construct some new Artin-Schelter regular algebras of global dimension 5. We prove that those algebras are all strongly noetherian, Auslander regular and Cohen-Macaulay, and describe their Nakayama automorphisms.

关键词： Artin-Schelter regular algebras graded Lie algebras Nakayama automorphisms

Totally geodesic submanifolds in compact Riemannian symmetric spaces and their stability

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Science China Mathematics 2000年第12期43卷 1279-1293页

作者：靳全勤 Institute of Applied Mathematics Academy of Mathematics and System Sciences Chinese Academy of SciencesBeijing 100080 China Department of Mathematics Hebei UniversityBaoding 071002China

In this paper, we determine a large class of totally geodesic submanifolds of a compact Riemannian symmetric *** stability of these submanifolds in their ambient space is also determined.

关键词： compact Riemannian symmetric spaces totally geodesic submanifolds involutive automorphisms of a Lie group (or a Lie algebra) stability.

Structures of Not-finitely Graded Lie Algebras Related to Generalized Heisenberg–Virasoro Algebras

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Acta Mathematica Sinica,English Series 2015年第10期31卷 1517-1530页

作者： Guang Zhe FAN Chen Hong ZHOU Xiao Qing YUE Department of Mathematics Tongji University

In this paper, we study the structure theory of a class of not-finitely graded Lie alge- bras related to generalized Heisenberg-Virasoro algebras. In particular, the derivation algebras, the automorphism groups and th... 详细信息

关键词： Not-finitely graded Lie algebras generalized Heisenberg-Virasoro algebras derivations automorphisms 2-cocycles

Applications of BGP-reflection functors: isomorphisms of cluster algebras

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Science China Mathematics 2006年第12期49卷 1839-1854页

作者： ZHU Bin Department of Mathematical Sciences Tsinghua UniversityBeijing 100084Chinae

Given a symmetrizable generalized Cartan matrix A,for any index k,one can define the matrix A (see sec.4 for the precise meaning).When A is of finite type,these isomorphisms behave nicely; they are compatible with the BGP-reflection functors of cluster categories defined in a previous work if we identify the indecomposable objects in the categories with cluster variables of the corresponding cluster algebras,and they are also compatible with the "truncated simple reflections" defined by *** the construction of preprojective or preinjective modules of hereditary algebras by Dlab-Ringel and the Coxeter automorphisms (i.e.a product of these isomorphisms),we construct infinitely many cluster variables for cluster algebras of infinite type and all cluster variables for finite types.

关键词： Coxeter automorphisms of cluster algebras,BGP-reflection functors,cluster variables.