Classification of Lie algebras of specific type in complexified Clifford algebras

被引：12

作者：

Shirokov, D. S. ^{[1
,2
]}

机构：

[1] Natl Res Univ Higher Sch Econ, Moscow, Russia

[2] Russian Acad Sci, Kharkevich Inst Informat Transmiss Problems, Moscow, Russia

来源：

LINEAR & MULTILINEAR ALGEBRA | 2018年 / 66卷 / 09期

关键词：

Clifford algebra; Lie algebra; quaternion type; Lie group; spin group; ELEMENTS;

D O I：

10.1080/03081087.2017.1376612

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a full classification of Lie algebras of specific type in complexified Clifford algebras. These 16 Lie algebras are direct sums of subspaces of quaternion types. We obtain isomorphisms between these Lie algebras and classical matrix Lie algebras in the cases of arbitrary dimension and signature. We present 16 Lie groups: one Lie group for each Lie algebra associated with this Lie group. We study connection between these groups and spin groups.

引用

页码：1870 / 1887

页数：18

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