Details:
Title  Hall and Gröbner bases and rewriting in free Lie algebras (Extended Abstract)  Author(s)  Willem A. de Graaf  Type  Technical Report, Misc  Abstract  This 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 LyndonShirshov 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. 
Language  English  Year  2005  Edition  0  Translation 
No  Refereed 
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