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Sibirskii Matematicheskii Zhurnal, 2005, Volume 46, Number 6, Pages 1302–1315 (Mi smj1040)  
This article is cited in 7 scientific papers (total in 7 papers)

Dual coalgebras of Jordan bialgebras and superalgebras

V. N. Zhelyabin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (259 kB) Citations (7)
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Abstract: W. Michaelis showed for Lie bialgebras that the dual coalgebra of a Lie algebra is a Lie bialgebra. In the present article we study an analogous question in the case of Jordan bialgebras. We prove that a simple infinite-dimensional Jordan superalgebra of vector type possesses a nonzero dual coalgebra. Thereby, we demonstrate that the hypothesis formulated by W. Michaelis for Lie coalgebras fails in the case of Jordan supercoalgebras.
Keywords: Hopf algebra, Lie bialgebra, Jordan bialgebra, Jordan superalgebra, nonassociative coalgebra, local finite dimensionality, dual coalgebra.
Received: 26.05.2004
English version:
Siberian Mathematical Journal, 2005, Volume 46, Issue 6, Pages 1050–1061
DOI: https://doi.org/10.1007/s11202-005-0099-6
Bibliographic databases:
UDC: 512.554
Language: Russian
Citation: V. N. Zhelyabin, “Dual coalgebras of Jordan bialgebras and superalgebras”, Sibirsk. Mat. Zh., 46:6 (2005), 1302–1315; Siberian Math. J., 46:6 (2005), 1050–1061
Citation in format AMSBIB
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\by V.~N.~Zhelyabin
\paper Dual coalgebras of Jordan bialgebras and superalgebras
\jour Sibirsk. Mat. Zh.
\yr 2005
\vol 46
\issue 6
\pages 1302--1315
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2195030}
\zmath{https://zbmath.org/?q=an:1118.17009}
\transl
\jour Siberian Math. J.
\yr 2005
\vol 46
\issue 6
\pages 1050--1061
\crossref{https://doi.org/10.1007/s11202-005-0099-6}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000234073700007}
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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