The Variety of Two-dimensional Algebras Over an Algebraically Closed Field

被引：47

作者：

Kaygorodov, Ivan ^{[1
]}

Volkov, Yury ^{[2
]}

机构：

[1] Univ Fed ABC, CMCC, Santo Andre, Brazil

[2] St Petersburg State Univ, St Petersburg, Russia

来源：

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2019年 / 71卷 / 04期

基金：

巴西圣保罗研究基金会;

关键词：

two-dimensional algebras; orbit closure; degeneration; rigid algebra; NILPOTENT LIE-ALGEBRAS; CLASSIFICATION; DEGENERATIONS; LEVEL; DEFORMATIONS;

D O I：

10.4153/S0008414X18000056

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The work is devoted to the variety of two-dimensional algebras over algebraically closed fields. First we classify such algebras modulo isomorphism. Then we describe the degenerations and the closures of certain algebra series in the variety of two-dimensional algebras. Finally, we apply our results to obtain analogous descriptions for the subvarieties of flexible and bicommutative algebras. In particular, we describe rigid algebras and irreducible components for these subvarieties.

引用

页码：819 / 842

页数：24

共 30 条

[11]

Gorbatsevich V.V., 1991, SOVIET MATH IZ VUZ, V35, P19

[12]

Gorbatsevich V. V., 1994, ST PETERSB MATH J, V5, P505

[13] On the level of some solvable Lie algebras [J].