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Subalgebras of free nilpotent and polynilpotent lie algebras
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dc.contributor.advisor | Robertson, E. F. | |
dc.contributor.author | Boral, Melih | |
dc.coverage.spatial | 153 p. | en_US |
dc.date.accessioned | 2018-06-05T13:28:54Z | |
dc.date.available | 2018-06-05T13:28:54Z | |
dc.date.issued | 1977 | |
dc.identifier.uri | https://hdl.handle.net/10023/13729 | |
dc.description.abstract | In this thesis we study subalgebras in free nilpotent and polynilpotent Lie algebras. Chapter 1 sets up the notation and includes definitions and elementary properties of free and certain reduced free Lie algebras that we use throughout this thesis. We also describe a Hall basis of a free Lie algebra as in [4] and a basis for a free polynilpotent Lie algebra which was developed in [24]. In Chapter 2 we first consider the class of nilpotency of subalbebras of free nilpotent Lie algebras starting with two-generator subalgebras. Then we study those subalgebras in a free nilpotent Lie algebra which, are themselves free nilpotent. We give necessary and sufficient conditions in the case of two-generator subalgebras. Chapter 3 extends the results obtained in Chapter 2 to the polynilpotent case. First we look at two-generator subalgebras of a free polynilpotent Lie algebra. Then we consider more general subalgebras. Finally we study those subalgebras which are themselves free polynilpotent and give necessary and sufficient conditions for two-generator subalgebras to be free polynilpotent. In Chapter 4 we first study certain properties of ideals in free, free nilpotent and free polynilpotent Lie algebras and establish the fact that in a free polynilpotent Lie algebra a nonzero ideal which is finitely-generated as a subalgebra must be equal to the whole algebra. Then we consider the quotient Lie algebra of a lower central term of a free Lie algebra by a term of the lower central series of an ideal. We then generalize the results to cover the free nilpotent and free polynilpotent cases. In the last section of Chapter 4 we consider ideals of free nilpotent (and later polynilpotent) Lie algebras as free nilpotent (polynilpotent) subalgebras and establish the fact that in most non-trivial cases such an ideal cannot be free nilpotent (polynilpotent). In the last chapter we consider the m+k-th term of the lower central series of a free Lie algebra as a subalgebra of the m-th term for m ⩽ k and generalize the results proved in [25]. We give reasons for the failure of these results in the case m > k. | en_US |
dc.language.iso | en | en_US |
dc.publisher | University of St Andrews | en |
dc.subject.lcc | QA252.3B7 | |
dc.subject.lcsh | Lie algebras | en |
dc.title | Subalgebras of free nilpotent and polynilpotent lie algebras | en_US |
dc.type | Thesis | en_US |
dc.contributor.sponsor | Turkey. Ministry of Education | en_US |
dc.type.qualificationlevel | Doctoral | en_US |
dc.type.qualificationname | PhD Doctor of Philosophy | en_US |
dc.publisher.institution | The University of St Andrews | en_US |
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