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Module structure on Lie powers and natural coalgebra-split sub-Hopf algebras of tensor algebras

Part of: Representation theory of groups Lie algebras and Lie superalgebras Hopf algebras, quantum groups and related topics Homotopy theory

Published online by Cambridge University Press:  04 April 2011

J. Y. Li ,
F. C. Lei  and
J. Wu
J. Y. Li
Affiliation:
Institute of Mathematics and Physics, Shijiazhuang Railway Institute, Shijiazhuang 050043, People's Republic of China (yanjinglee@163.com)
F. C. Lei
Affiliation:
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, People's Republic of China (fclei@dlut.edu.cn)
J. Wu
Affiliation:
Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, Singapore 119076 (matwuj@nus.edu.sg)
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Abstract

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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.

Keywords

tensor algebrasLie powerscoalgebrassub-Hopf algebrasTn-projective functorsnatural coalgebra decompositions

MSC classification

Secondary: 55P35: Loop spaces 16T15: Coalgebras and comodules; corings 17B60: Lie (super)algebras associated with other structures (associative, Jordan, etc.) 20C30: Representations of finite symmetric groups 55P65: Homotopy functors
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 54 , Issue 2 , June 2011 , pp. 467 - 504
Copyright
Copyright © Edinburgh Mathematical Society 2011

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