## Dual Lie elements and a derivation for the cofree coassociative coalgebra

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- by Gary Griffing
- Proc. Amer. Math. Soc.
**123**(1995), 3269-3277 - DOI: https://doi.org/10.1090/S0002-9939-1995-1273493-6
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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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## Bibliographic Information

- © Copyright 1995 American Mathematical Society
- 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