Classification of Six Dimensional Solvable Indecomposable Lie Algebras with a codimension one nilradical over R |
Posted on:2012-03-18 | Degree:Ph.D | Type:Dissertation |
University:The University of Toledo | Candidate:Shabanskaya, Anastasia | Full Text:PDF |
GTID:1450390008491425 | Subject:Mathematics |
Abstract/Summary: | |
In my dissertation I am looking at six dimensional Lie algebras which are solvable, indecomposable and that have a five-dimensional nilradical. Such algebras were classified by the Russian mathematician G. M. Mubarakzyanov in a paper published in 1963. Depending on the structure of the five dimensional nilradical his paper has nine paragraphs.;The paper contains errors because calculations were done by hand and the list of algebras is incomplete. Also some of his Lie algebras are isomorphic between themselves. I made extensive use of MAPLE with some routines to help finesse Mubarakzyanov's list. Precisely, I corrected all the misprints and completed his list of algebras: in Paragraph 6 he disregarded a case which gives two new Lie algebras. There is also one new Lie algebra in Paragraph 2, one in Paragraph 5 and two new Lie algebras in Paragraph 7. |
Keywords/Search Tags: | Lie algebras, Six dimensional, Solvable indecomposable, Nilradical, Paragraph |
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