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Moscow Mathematical Journal, 2008, Volume 8, Number 4, Pages 647–666
DOI: https://doi.org/10.17323/1609-4514-2008-8-4-647-666
(Mi mmj324)
 

This article is cited in 19 scientific papers (total in 19 papers)

Local Structure of Algebraic Monoids

M. Brion

Institut Fourier, UFR de Mathématiques
Full-text PDF Citations (19)
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Abstract: We describe the local structure of an irreducible algebraic monoid $M$ at an idempotent element $e$. When $e$ is minimal, we show that $M$ is an induced variety over the kernel $MeM$ (a homogeneous space) with fibre the two-sided stabilizer $M_e$ (a connected affine monoid having a zero element and a dense unit group). This yields the irreducibility of stabilizers and centralizers of idempotents when $M$ is normal, and criteria for normality and smoothness of an arbitrary monoid $M$. Also, we show that $M$ is an induced variety over an abelian variety, with fiber a connected affine monoid having a dense unit group.
Key words and phrases: algebraic monoid, idempotent, local structure, induced variety.
Received: October 6, 2007
Bibliographic databases:
Language: English
Citation: M. Brion, “Local Structure of Algebraic Monoids”, Mosc. Math. J., 8:4 (2008), 647–666
Citation in format AMSBIB
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\by M.~Brion
\paper Local Structure of Algebraic Monoids
\jour Mosc. Math.~J.
\yr 2008
\vol 8
\issue 4
\pages 647--666
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\crossref{https://doi.org/10.17323/1609-4514-2008-8-4-647-666}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2499350}
\zmath{https://zbmath.org/?q=an:1170.14035}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000261829900003}
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  • This publication is cited in the following 19 articles:
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