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sub-hopf algebras

Proceedings of the Edinburgh Mathematical Society (1)

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Module structure on Lie powers and natural coalgebra-split sub-Hopf algebras of tensor algebras
Part of
J. Y. Li, F. C. Lei, J. Wu
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 54 / Issue 2 / June 2011

Published online by Cambridge University Press:

04 April 2011, pp. 467-504
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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.