On Lie Triple Systems.pdf

1、In this report, we shall give a structure theory of Lie triple systems in the first part as a collection of the work have been done including the relation between Lie triple systems and Lie algebras(Jordan algebras), so

2、me results on the solvable, the nilpotent and the semi-simple. Invariant bilinear forms will be also concerned. The second part we shall mainly connect Lie triple systems with some other algebras and then try to find mor

3、e new results on Lie triple systems. W.G. Lister proved that a semi-simple Lie triple system can decomposed into direct sum of simple Lie triple systems with the tool of standard imbedding Lie algebra and gave the uniqu

4、eness of the decomposition. In the first section of this part we shall give the uniqueness of decomposition from Lie triple system's structure directly, and cover the result of the uniqueness of semi-simple Lie triple sy

5、stems. In section part we shall discuss some properties of the tensor product of a communicative associative algebra and a Lie triple system, and then construct some finite dimensional Lie triple systems from Laurent-po

6、lynomial algebra and Novikov algebra. L. J. Santharouabane gave the definition of nilpotent Lie algebras of maximal rank and have shown some relationships between Kac-Moody algebras and such special kind of nilpotent Li

7、e algebras as follows. For any nilpotent Lie algebra g of maximal rank and of type l ,with a minimal system of generators X = {e1, e2,… el}, there exists an l × l generalized Cartan matrix A =(aij) whose equivalence cl

8、ass is an invariant of g such that (adei)-aijej ≠ 0, (adei)-aij+1ej = 0. Therefore, from the Kac-Moody algebra g(A) associated to A, a special kind of nilpotent Lie algebr