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Sibirskii Matematicheskii Zhurnal, 2003, Volume 44, Number 1, Pages 87–111 (Mi smj1170)  

This article is cited in 7 scientific papers (total in 7 papers)

Jordan (super)coalgebras and Lie (super)coalgebras

V. N. Zhelyabin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (343 kB) Citations (7)
References:
Abstract: We discuss the question of local finite dimensionality of Jordan supercoalgebras. We establish a connection between Jordan and Lie supercoalgebras which is analogous to the Kantor–Köecher–Tits construction for ordinary Jordan superalgebras. We exhibit an example of a Jordan supercoalgebra which is not locally finite-dimensional. Show that, for a Jordan supercoalgebra $(J,\Delta)$ with a dual algebra $J^*$, there exists a Lie supercoalgebra $(L^c(J),\Delta_L)$ whose dual algebra $(L^c(J))^*$ is the Lie $KKT$-superalgebra for the Jordan superalgebra $J^*$. It is well known that some Jordan coalgebra $J^0$ can be constructed from an arbitrary Jordan algebra $J$. We find necessary and sufficient conditions for the coalgebra $(L^c(J^0),\Delta_L)$ to be isomorphic to the coalgebra $(\operatorname{Loc}(L_{\textup{in}}(J)^0),\Delta^0_L)$, where $L_{\textup{in}}(J)$ is the adjoint Lie $KKT$-algebra for the Jordan algebra $J$.
Keywords: Jordan superalgebra, Lie superalgebra, Kantor–Köcher–Tits construction, Jordan coalgebra, Lie coalgebra.
Received: 25.02.2002
English version:
Siberian Mathematical Journal, 2003, Volume 44, Issue 1, Pages 73–92
DOI: https://doi.org/10.1023/A:1022064320856
Bibliographic databases:
UDC: 512.554
Language: Russian
Citation: V. N. Zhelyabin, “Jordan (super)coalgebras and Lie (super)coalgebras”, Sibirsk. Mat. Zh., 44:1 (2003), 87–111; Siberian Math. J., 44:1 (2003), 73–92
Citation in format AMSBIB
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\by V.~N.~Zhelyabin
\paper Jordan (super)coalgebras and Lie (super)coalgebras
\jour Sibirsk. Mat. Zh.
\yr 2003
\vol 44
\issue 1
\pages 87--111
\mathnet{http://mi.mathnet.ru/smj1170}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1967609}
\zmath{https://zbmath.org/?q=an:1049.17029}
\transl
\jour Siberian Math. J.
\yr 2003
\vol 44
\issue 1
\pages 73--92
\crossref{https://doi.org/10.1023/A:1022064320856}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000181022100008}
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  • https://www.mathnet.ru/eng/smj/v44/i1/p87
  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Сибирский математический журнал Siberian Mathematical Journal
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