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This article is cited in 19 scientific papers (total in 19 papers)
Local Structure of Algebraic Monoids
M. Brion Institut Fourier, UFR de Mathématiques
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
Citation:
M. Brion, “Local Structure of Algebraic Monoids”, Mosc. Math. J., 8:4 (2008), 647–666
Linking options:
https://www.mathnet.ru/eng/mmj324 https://www.mathnet.ru/eng/mmj/v8/i4/p647
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Abstract page: | 237 | References: | 78 |
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