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Construction of Free Lie Algebras

  • Andrea BonfiglioliEmail author
  • Roberta Fulci
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2034)

Abstract

THE aim of this chapter is twofold. On the one hand (Sect. 8.1), we complete the missing proof from Chap. 2 concerning the existence of a free Lie algebra Lie(X) related to a set X. This proof relies on the direct construction of Lie(X) as a quotient of the free non-associative algebra Lib(X). Furthermore, we prove that Lie(X) is isomorphic to L(K_X_), and the latter provides a free Lie algebra over X.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BolognaBolognaItaly

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