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Mahmood Alam

Cartan Subalgebras of Locally Finite Lie Algebras

Mathematik

ISBN 978-3-8322-7849-6

Review

Zentralblatt MATH 1207 | 1, 21.11.2011

www.zentralblatt-math.org

In this dissertation, the author investigates the cohomology spaces of locally nilpotent Lie algebras with values in a weakly locally _nite module of a locally nilpotent Lie algebra, due to the natural importance of cohomology spaces in such a case. The work, which contains a dissertation of almost 80 pages, is divided into three Chapters. In the _rst of them the author deals with the basic notions of Lie algebras Theory and Cohomology of Lie algebras. He introduces a new concept which he calls ad-splittability of locally nilpotent Lie algebras. Chapter 2 is devoted to deal with the cohomology spaces of nilpotent and locally nilpotent Lie algebras. The author proves some results related to the vanishing of cohomology spaces of these algebras. Finally, in Chapter 3, the author investigates the conjugacy classes of splitting Cartan subalgebras and maximal toral subalgebras of ad-splittable locally solvable and those ad-splittable Lie algebras which are non-abelian extensions of locally nilpotent Lie algebras. Juan N_u~nez Vald_es (Sevilla)

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