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Nonabelian Generalized Lax Pairs, the Classical Yang-Baxter Equation and PostLie Algebras

Author: NiXiang
Tutor: BaiChengMing
School: Nankai University
Course: Basic mathematics
Keywords: Lax pair Lie algebra Lie bialgebra (?)-operator classical Yang-Baxter equation PostLie algebra
CLC: O152.5
Type: Master's thesis
Year: 2010
Downloads: 45
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Abstract


We generalize the classical study of (generalized) Lax pairs, the related (?)-operators and the (modified) classical Yang-Baxter equation by introducing the con-cepts of nonabelian generalized Lax pairs, extended (?)-operators and the extended classical Yang-Baxter equation. We study in this context the nonabelian generalized r-matrix ansatz and the related double Lie algebra structures. Relationship between extended (?)-operators and the extended classical Yang-Baxter equation is estab-lished, especially for self-dual Lie algebras. This relationship allows us to obtain explicit description of the Manin triples for a new class of Lie bialgebras. Further-more, we show that a natural structure of PostLie algebra is behind (?)-operators and fits in a setup of triple Lie algebra that produces self-dual nonabelian generalized Lax pairs.

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