Y. Barnea and D. S. Passman (2007) Filtrations in semisimple lie Algebras, II. Transactions of the American Mathematical Society, 360 (2). pp. 801-817. ISSN 0002-9947
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In this paper, we continue our study of the maximal bounded Z-filtrations of a complex semisimple Lie algebra L. Specifically, we discuss the functionals which give rise to such filtrations, and we show that they are related to certain semisimple subalgebras of L of full rank. In this way, we determine the “order” of these functionals and count them without the aid of computer computations. The main results here involve the Lie algebras of type E6, E7 and E8, since we already know a good deal about the functionals for the remaining types. Nevertheless, we reinterpret our previous results into the new context considered here. Finally, we describe the associated graded Lie algebras of all of the maximal filtrations obtained in this manner.
This is a Published version This version's date is: 18/09/2007 This item is peer reviewed
https://repository.royalholloway.ac.uk/items/3717d7da-54d9-7c0f-880e-c3ae9cbc9ca3/1/
Deposited by Al Dean (ZSRA118) on 22-Feb-2010 in Royal Holloway Research Online.Last modified on 18-Jan-2011
(C) 2007, American Mathematical Society, whose permission to mount this version for private study and research is acknowledged. The repository version is the author's final draft. The copyright for this article reverts to public domain after 28 years from publication.
First published in Transactions of the American Mathematical Society in 2006, published by the American Mathematical Society.
[BP] Y. Barnea and D. S. Passman, Filtrations in semisimple Lie algebras, I, Trans. AMS, 358(2006), 1983-2010. MR2197439 (2007a:17013)
[Bo] N. Bourbaki, Lie Groups and Lie Algebras: Chapters 4-6, Springer-Verlag, Berlin, 2002.MR1890629 (2003a:17001)
[D] E. B. Dynkin, Semisimple subalgebras of semisimple Lie algebras, AMS Translations (2) 6 (1957), 111-244.
[H] J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, second printing, Springer-Verlag, New York, 1972. MR0323842 (48:2197)
[K] V. G. Kac, Infinite Dimensional Lie Algebras, Cambridge Univ. Press, Cambridge, 1990.MR1104219 (92k:17038)