Christodoulou, Costa Andrew (1979) Profinite Lie algebras. PhD thesis, University of Warwick.

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Abstract

It is well-known that the theory of finite dimensional Lie algebras is similar in many ways to the theory of finite groups. Noting the way that finite groups are generalised to certain periodic FC-groups (see Baer, [2], for example), we can likewise generalise finite dimensional Lie algebras; alternatively we can study ideally finite Lie algebras by using ideas from the theory of periodic FG-groups, drawing analogies as far as possible (see Stewart, [15], for example).

We can also extend the theory of finite groups to profinite groups (see for example Hartley, [6]) using the ideas and methods used for finite groups and periodic FC-groups. In this thesis we study profinite Lie algebras from two viewpoints: by using the ideas and methods of ideally finite Lie algebras, and by analogy with profinite groups.

Some of the ideas can be traced to the corresponding situation for algebraic groups, that is pro-affine algebraic groups (see Hochschild, [7], and Hochschild and Mostow, [8]), for example the definition of coset topology in Hochschild and Mostow, p1130, suggests the definition of the affine topology.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Lie algebras, Infinite dimensional Lie algebras, Profinite groups
Official Date:	April 1979
Dates:	Date Event April 1979 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Stewart, Ian ; Hartley, B.
Extent:	223 leaves
Language:	eng

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