On the Lie enveloping algebra of a pre-Lie algebra
2008 ◽
Vol 2
(1)
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pp. 147-167
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Keyword(s):
AbstractWe construct an associative product on the symmetric module S(L) of any pre-Lie algebra L. It turns S(L) into a Hopf algebra which is isomorphic to the enveloping algebra of LLie. Then we prove that in the case of rooted trees our construction gives the Grossman-Larson Hopf algebra, which is known to be the dual of the Connes-Kreimer Hopf algebra. We also show that symmetric brace algebras and pre-Lie algebras are the same. Finally, we give a similar interpretation of the Hopf algebra of planar rooted trees.
2009 ◽
Vol 20
(03)
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pp. 339-368
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Keyword(s):
2008 ◽
Vol 18
(02)
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pp. 271-283
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Keyword(s):
2010 ◽
Vol 82
(3)
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pp. 401-423
Keyword(s):
1968 ◽
Vol 20
◽
pp. 344-361
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1996 ◽
Vol 120
(2)
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pp. 193-206