The structure theorem for weak module coalgebras

Authors: Wang, Yu.¹; Zhang, L.²

Source: Mathematical Notes, Volume 88, Numbers 1-2, August 2010 , pp. 3-15(13)

Publisher: Springer

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Abstract:

Let H be a weak Hopf algebra, let C be a weak right H-module coalgebra, and let <EquationSource Format="TEX">$$ bar C = {C mathord{left/ {vphantom {C C}} right. kern-ulldelimiterspace} C} cdot Ker sqcap ^L $$</EquationSource> . We prove a structure theorem for weak module coalgebras, namely, C is isomorphic as a weak right H-module coalgebra to a weak smash coproduct <EquationSource Format="TEX">$$ bar C $$</EquationSource> × H defined on a k-space if there exists a weak right H-module coalgebra map Φ: C → H.

Keywords: weak Hopf algebra; weak Hopf bicomodule; weak comodule coalgebra; weak smash coproduct; weak module coalgebra

Document Type: Research article

DOI: http://dx.doi.org/10.1134/S0001434610070011

Affiliations: 1: Nanjing Agricultural University, Nanjing, China 2: Nanjing Agricultural University, Nanjing, China, Email: zlyun@njau.edu.cn

Publication date: 2010-08-01