Three types of derivation lie algebras of isolated hypersurface singularities

被引:0
作者
Hussain, Naveed [1 ]
Yau, Stephen S. -T. [2 ,3 ]
Zuo, Huaiqing [3 ]
机构
[1] Univ Agr Faisalabad, Dept Math & Stat, Faisalabad 38000, Punjab, Pakistan
[2] Yanqi Lake Beijing Inst Math Sci & Applicat, Beijing 101400, Peoples R China
[3] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
关键词
Isolated hypersurface singularity; Lie algebra; Moduli algebra; NEGATIVE WEIGHT DERIVATIONS; 4D N=2 SCFT; GENERALIZED CARTAN-MATRICES; MODULI ALGEBRAS; COMPLEX STRUCTURES; NONEXISTENCE; CONJECTURE; INVARIANT; DUALITY; IDEALS;
D O I
10.1007/s12215-024-01182-5
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In our previous work, we introduced three different ways to associate Lie algebras to isolated hypersurface singularities. In this paper, we analyze their relations in the case of weighted homogeneous singularities. Moreover, explicit formulas of the dimensions of three series of Lie algebras are given for fewnomial singularities. Several conjectures are proposed and verified partially.
引用
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页数:20
相关论文
共 45 条
[1]  
Almirón P, 2021, Arxiv, DOI arXiv:1910.12843
[2]   A note on a question of Dimca and Greuel [J].
Almiron, Patricio ;
Blanco, Guillem .
COMPTES RENDUS MATHEMATIQUE, 2019, 357 (02) :205-208
[3]  
Benson M., 1986, ADV STUDIES PURE MAT, V8, P3, DOI DOI 10.2969/ASPM/00810003
[4]   DETERMINATION OF DIFFERENTIABLY SIMPLE RINGS WITH A MINIMAL IDEAL [J].
BLOCK, RE .
ANNALS OF MATHEMATICS, 1969, 90 (03) :433-&
[5]  
Chen BY, 2021, MATH RES LETT, V28, P1, DOI [10.4310/mrl.2021.v28.n1.a1, 10.4310/MRL.2021.v28.n1.a1]
[6]   VARIATION OF COMPLEX STRUCTURES AND VARIATION OF LIE ALGEBRAS II: NEW LIE ALGEBRAS ARISING FROM SINGULARITIES [J].
Chen, Bingyi ;
Hussain, Naveed ;
Yau, Stephen S-T ;
Zuo, Huaiqing .
JOURNAL OF DIFFERENTIAL GEOMETRY, 2020, 115 (03) :437-473
[7]   THE NONEXISTENCE OF NEGATIVE WEIGHT DERIVATIONS ON POSITIVE DIMENSIONAL ISOLATED SINGULARITIES: GENERALIZED WAHL CONJECTURE [J].
Chen, Bingyi ;
Chen, Hao ;
Yau, Stephen S-T ;
Zuo, Huaiqing .
JOURNAL OF DIFFERENTIAL GEOMETRY, 2020, 115 (02) :195-224
[8]   4d N=2 SCFT and singularity theory Part III: Rigid singularity [J].
Chen, Bingyi ;
Xie, Dan ;
Yau, Stephen S-T ;
Yau, Shing-Tung ;
Zuo, Huaiqing .
ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS, 2018, 22 (08) :1885-1905
[9]   4d N=2 SCFT and singularity theory Part II: complete intersection [J].
Chen, Bingyi ;
Xie, Dan ;
Yau, Shing-Tung ;
Yau, Stephen S. -T. ;
Zuo, Huaiqing .
ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS, 2017, 21 (01) :121-145
[10]   Nonexistence of negative weight derivations on graded artin algebras: A conjecture of halperin [J].
Chen, H .
JOURNAL OF ALGEBRA, 1999, 216 (01) :1-12