Standard Lyndon bases of Lie algebras and enveloping algebras (1995) [5 citations — 0 self]
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author = {Pierre Lalonde and Pierre Lalonde and Arun Ram and Arun Ram},
title = {Standard Lyndon bases of Lie algebras and enveloping algebras},
journal = {Trans. Am. Math. Soc., number},
year = {1995},
volume = {347},
pages = {1821--1830}
}
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Abstract:
n words and the free Lie algebra In this section we give a short summary of the facts about Lyndon words and the free Lie algebra which Research supported by FCAR and NSERC grants. Partially supported by a National Science Foundation Postdoctoral Fellowship. we shall use. All of the facts in this section are well known. A comprehensive treatment of free Lie algebras (and Lyndon words) appears in the book by C. Reutenauer [Re]. Let A be an ordered alphabet and let A be the set of all words in the alphabet A (the free monoid generated by A). Let juj denote the length of the word u 2 A and let u ! v denote that the word u is lexicographically smaller than the word v. A word ` 2 A is a Lyndon word if it is lexicographically smaller than all its cyclic rearrangements. Let ` be a Lyndon word and let m;n be words such that ` = mn and n is the longest Lyndon word appearing as a proper right factor of `. Then m is also a Lyndon word ([Lo] Prop 5.1.3). The standard bracketing of a
Citations
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