What are the motivations and examples of P. Hall Family?

Question

I am reading J. P. Serre's Lie Algebras and Lie Groups and here is how a P. Hall Family is defined:

I failed to understand the motivations of this definition. Could anyone explain it to me? Also, some simple examples of P. Hall Families will also be greatly appreciated.

Dietrich Burde · Answer 1 · 2019-07-24T15:08:39.817

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This is important, for example, for the theory of free Lie algebras, e.g., a P. Hall basis. As with all definitions, the motivation comes afterwards, rarely before. A good reference is the book Free Lie algebras by Christophe Reutenauer. However, also the book J.-P. Serre you are reading gives motivating results afterwards. For an example, see

Examples of Free Lie Algebra

edited Jul 24 '19 at 15:08

answered Jul 24 '19 at 14:52

Dietrich Burde

140,055

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Thank you so much for your answer! – Zuriel Jul 24 '19 at 14:54
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Dort haben Sie meine Frage vor 4 Jahren beantwortet. Danke nochmal! – Zuriel Jul 24 '19 at 16:35
Ja, ich habe es auch gesehen :) – Dietrich Burde Jul 24 '19 at 18:02

What are the motivations and examples of P. Hall Family?

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