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TitleHall and Gröbner bases and rewriting in free Lie algebras (Extended Abstract)
Author(s) Willem A. de Graaf
TypeTechnical Report, Misc
AbstractThis document is organized as follows. In Section 2 a class of bases of the free Lie algebra, called Hall sets, is described and we indicate how to multiply two basis elements. In Section 3 we consider the problem of rewriting in the free Lie algebra. We show that we can do this if we can decide whether a given basis element is a factor of another basis element. Then in Section 4 we describe two particular Hall sets for which we can decide this. The first of these is known as the set of Lyndon-Shirshov words. The second is to the best of our knowledge not described elsewhere. Then in Section 5 we sketch some Groebner bases theory for the free Lie algebra, and we state a theorem by A. I. Shirshov giving a sucient condition for a set to be a Groebner basis. Finally in Section 6 we use this theorem to give a short proof of a (rather classical) theorem in the theory of Lie algebras.
Translation No
Refereed No