Module Structure on Lie Powers and Natural Coalgebra-Split Sub Hopf Algebras of Tensor Algebras

Details Module Structure on Lie Powers and Natural Coalgebra-Split Sub Hopf Algebras of Tensor Algebras Module Structure on Lie Powers and Natural Coalgebra-Split Sub Hopf Algebras of Tensor Algebras

2010-02-02

arxiv.org/abs/1002.0434v1

Mathematics

Algebraic Topology

33 pages

Scientific paper

In this article, we investigate the functors from modules to modules that occur as the summands of tensor powers and the functors from modules to Hopf algebras that occur as natural coalgebra summands of tensor algebras. The main results provide some explicit natural coalgebra summands of tensor algebras. As a consequence, we obtain some decompositions of Lie powers over the general linear groups.

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