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Elementary and ф-free Lie Triple Systems

Author: LiuLiLi
Tutor: BaiRuiPu
School: Hebei University
Course: Basic mathematics
Keywords: Heisenberg n-Lie algebra automorphism group Lie triple system elementary Lie triple system Φ-free Lie triple system
CLC: O152.5
Type: Master's thesis
Year: 2009
Downloads: 4
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Abstract


This thesis mainly discusses two questions. In the first question, we concern Heisen-berg n-Lie algebras, prove that two Heisenberg n-Lie algebras may not be isomorphic if they have the same dimension. We also determine the structures of automorphism groups of (3m+1)-dimensional Heisenberg 3-Lie algebras and(mn+1)-dimensional Heisenberg n-Lie algebras, and give the concrete expression of the automorphisms. In the second question, we give the concepts of elementary andΦ-free Lie triple systems, and investigate the structures of them and the relation between them.Section 1 recalls some definitions and notations used in section 2. Section 2 deter-mines the structures of automorphism groups of (3m+1)-dimensional Heisenberg 3-Lie algebras and (mn+1)-dimensional Heisenberg n-Lie algebras and gives the concrete expression of the automorphisms. Section 3 gives the notions and some basic facts of Lie triple systems. Section 4 discusses the structures of elementary Lie triple systems. Section 5 describes some properties ofΦ-free Lie triple systems. Section 6 describes the relations between elementary andΦ-free Lie triple systems.

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Group theory > Lie group
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