Short (SL2 x SL2)-structures on Lie algebras

被引：0

作者：

Beites, Patricia D. ^{[1
,2
]}

Cordova-Martinez, Alejandra S. ^{[3
,4
,5
]}

Cunha, Isabel ^{[1
,2
]}

Elduque, Alberto ^{[4
,5
]}

机构：

[1] Univ Beira Interior, Dept Matemat, P-6201001 Covilha, Portugal

[2] Univ Beira Interior, Ctr Matemat & Aplicacoes, P-6201001 Covilha, Portugal

[3] Univ Malaga, Dept Matemat Aplicada, ETS Ingn Informat, Malaga 29071, Spain

[4] Univ Zaragoza, Dept Matemat, Zaragoza 50009, Spain

[5] Univ Zaragoza, Inst Univ Matemat & Aplicac, Zaragoza 50009, Spain

来源：

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2024年 / 118卷 / 02期

关键词：

S-structures; J-ternary algebras; Structurable algebras; TERNARY ALGEBRAS; CONSTRUCTION; S-4-ACTION; SYSTEMS;

D O I：

10.1007/s13398-023-01541-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

S-structures on Lie algebras, introduced by Vinberg, represent a broad generalization of the notion of gradings by abelian groups. Gradings by, not necessarily reduced, root systems provide many examples of natural S-structures. Here we deal with a situation not covered by these gradings: the short (SL2 x SL2)-structures, where the reductive group is the simplest semisimple but not simple reductive group. The algebraic objects that coordinatize these structures are the J-ternary algebras of Allison, endowed with a nontrivial idempotent.

引用

页数：21

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