Alternative M2-algebras and Γ-algebras

被引：0
|
作者：
Grishkov, A. [1 ]
Shestakov, I. [1 ]
机构：
[1] Univ Sao Paulo, Sao Paulo, Brazil
来源：
SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES | 2024年 / 18卷 / 02期
基金：
巴西圣保罗研究基金会;
关键词：
Alternative algebra; Coordinatization theorem; Category of M-2-algebras; Jordan superalgebra; Grassmanian; JORDAN SUPERALGEBRAS; REPRESENTATIONS;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Recently V. H. Lopez Solis and I. Shestakov [9] solved an old problem by N.Jacobson [2] on describing of unital alternative algebras containing the matrix 2x2 algebra M(2 )as a unital subalgebra. Here we give another description of M-2-algebras via the 6-dimensional alternative superalgebra B(4, 2) and an auxiliar Z2-graded algebra Gamma. It occurs that the category of alternative M-2-algebras is isomorphic to the category of Gamma-algebras. We describe also the free Gamma-algebras and construct their bases.
引用
收藏
页码：696 / 709
页数：14
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