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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Dual Lie elements and a derivation for the cofree coassociative coalgebra


Author: Gary Griffing
Journal: Proc. Amer. Math. Soc. 123 (1995), 3269-3277
MSC: Primary 16W30
DOI: https://doi.org/10.1090/S0002-9939-1995-1273493-6
MathSciNet review: 1273493
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Abstract: We construct a derivation D in the Hopf algebra TcV, the cofree coassociative coalgebra on a vector space V. We then define the subspace of TcV consisting of dual Lie elements, which is analogous to the subspace of the Hopf algebra TV, the free associative algebra on V, consisting of Lie elements. Thereafter, we formulate a dual Dynkin-Specht-Wever theorem. Using our map D, we then give very short proofs of both the dual Dynkin-Specht-Wever and dual Friedrichs' theorems, each of which characterizes the space of dual Lie elements in TcV at characteristic 0.


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DOI: https://doi.org/10.1090/S0002-9939-1995-1273493-6
Article copyright: © Copyright 1995 American Mathematical Society