Quasi-deformations of Si2(F) using twisted derivations

被引：67

作者：

Larsson, Daniel ^{[2
]}

Silvestrov, Sergei D. ^{[1
]}

机构：

[1] Lund Univ, Ctr Math Sci, SE-22100 Lund, Sweden

[2] Uppsala Univ, Dept Math, S-75238 Uppsala, Sweden

来源：

COMMUNICATIONS IN ALGEBRA | 2007年 / 35卷 / 12期

关键词：

quasi-deformations; quasi-lie algebras; twisted derivation; twisted jacobi identity;

D O I：

10.1080/00927870701545127

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article we apply a method devised in Hartwig, Larsson, and Silvestrov (2006) and Larsson and Silvestrov (2005a) to the simple 3-dimensional Lie algebra sI(2)(F). One of the main points of this deformation method is that the deformed algebra comes endowed with a canonical twisted Jacobi identity. We show in the present article that when our deformation scheme is applied to sI(2)(F) we can, by choosing parameters suitably, deform sI(2)(F) into the Heisenberg Lie algebra and some other 3-dimensional Lie algebras in addition to more exotic types of algebras, this being in stark contrast to the classical deformation schemes where sI(2)(F) is rigid.

引用

页码：4303 / 4318

页数：16

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