n-ary Algebras of the First Level

被引：5
作者：
Volkov, Yury [1 ]
机构：
[1] St Petersburg State Univ, Univ Skaya Nab 7-9, St Petersburg, Russia
来源：
MEDITERRANEAN JOURNAL OF MATHEMATICS | 2022年 / 19卷 / 01期
基金：
俄罗斯科学基金会;
关键词：
n-ary algebra; level of algebra; orbit closure; degeneration; CLASSIFICATION;
D O I：
10.1007/s00009-021-01894-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
n-ary algebras of the first degeneration level are described. A detailed classification is given in the cases n = 2, 3.
引用
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页数：16
相关论文
共 12 条
[1]   Classification of orbit closures of 4-dimensional complex Lie algebras [J].
Burde, D ;
Steinhoff, C .
JOURNAL OF ALGEBRA, 1999, 214 (02) :729-739
[2]   Contractions of Filippov algebras [J].
de Azcarraga, Jose A. ;
Izquierdo, Jose M. ;
Picon, Moises .
JOURNAL OF MATHEMATICAL PHYSICS, 2011, 52 (01)
[3]  
Gorbatsevich V., 1991, SOV MATH IZ VUZ, V35, P17
[4]  
Gorbatsevich V., 1994, ST PETERSB MATH J, V5, P505
[5]   ON THE CONTRACTION OF GROUPS AND THEIR REPRESENTATIONS [J].
INONU, E ;
WIGNER, EP .
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1953, 39 (06) :510-524
[6]  
Kaygorodov I., 2020, DEGENERATIONS FILIPP
[7]   COMPLETE CLASSIFICATION OF ALGEBRAS OF LEVEL TWO [J].
Kaygorodov, Ivan ;
Volkov, Yury .
MOSCOW MATHEMATICAL JOURNAL, 2019, 19 (03) :485-521
[8]   The Variety of Two-dimensional Algebras Over an Algebraically Closed Field [J].
Kaygorodov, Ivan ;
Volkov, Yury .
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2019, 71 (04) :819-842
[9]   The classification of algebras of level one [J].
Khudoyberdiyev, A. Kh. ;
Omirov, B. A. .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2013, 439 (11) :3460-3463
[10]   On Deformations of n-Lie Algebras [J].
Makhlouf, Abdenacer .
NON-ASSOCIATIVE AND NON-COMMUTATIVE ALGEBRA AND OPERATOR THEORY, NANCAOT, 2016, 160 :55-81
12