Classification of Novikov algebras

被引：34

作者：

Burde, Dietrich ^{[1
]}

de Graaf, Willem ^{[2
]}

机构：

[1] Univ Vienna, Fak Math, A-1090 Vienna, Austria

[2] Univ Trent, Dipartimento Matemat, I-38050 Trento, Italy

来源：

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING | 2013年 / 24卷 / 01期

基金：

奥地利科学基金会;

关键词：

Novikov algebras; Classification; Computational methods; SOLVABLE LIE-ALGEBRAS; COMMUTATIVE ALGEBRAS;

D O I：

10.1007/s00200-012-0180-x

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We describe a method for classifying the Novikov algebras with a given associated Lie algebra. Subsequently we give the classification of the Novikov algebras of dimension 3 over and , as well as the classification of the 4-dimensional Novikov algebras over whose associated Lie algebra is nilpotent. In particular this includes a list of all 4-dimensional commutative associative algebras over .

引用

页码：1 / 15

页数：15

共 15 条

[1] [Anonymous], 1992, IDEALS VARIETIES ALG, DOI DOI 10.1007/978-1-4757-2181-2
[2] DIFFERENTIAL CALCULI ON COMMUTATIVE ALGEBRAS
BAEHR, HC
DIMAKIS, A
MULLERHOISSEN, F
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1995, 28 (11): : 3197 - 3222
[3] Transitive Novikov algebras on four-dimensional nilpotent Lie algebras
Bai, CM
Meng, DJ
[J]. INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 2001, 40 (10) : 1761 - 1768
[4] The classification of Novikov algebras in low dimensions
Bai, CM
Meng, DJ
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2001, 34 (08): : 1581 - 1594
[5] The Magma algebra system .1. The user language
Bosma, W
Cannon, J
Playoust, C
[J]. JOURNAL OF SYMBOLIC COMPUTATION, 1997, 24 (3-4) : 235 - 265
[6] Burde D., 2006, Cent. Eur. J. Math., V4, P323
[7] Novikov algebras and Novikov structures on Lie algebras
Burde, Dietrich
Dekimpe, Karel
Vercammen, Kim
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2008, 429 (01) : 31 - 41
[8] Novikov structures on solvable Lie algebras
Burde, Dietrich
Dekimpe, Karel
[J]. JOURNAL OF GEOMETRY AND PHYSICS, 2006, 56 (09) : 1837 - 1855
[9] Burde D, 2009, CONTEMP MATH, V491, P125
[10] de Graaf W. A., 2010, ARXIV10095339V1MATHR

← 1 2 →