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Transactions of the Moscow Mathematical Society

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On complex weakly commutative homogeneous spaces


Author: I. V. Losev
Translated by: O. A. Khleborodova
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 67 (2006).
Journal: Trans. Moscow Math. Soc. 2006, 199-223
MSC (2000): Primary 53C30; Secondary 22F30, 53D05
DOI: https://doi.org/10.1090/S0077-1554-06-00155-5
Published electronically: December 27, 2006
MathSciNet review: 2301594
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Abstract: Let $ G$ be a complex algebraic group and $ L$ an algebraic subgroup of $ G$. The quotient space $ G/L$ is called weakly commutative if a generic orbit of the action $ G:T^*(G/L)$ is a coisotropic submanifold. We classify weakly commutative homogeneous spaces $ N\leftthreetimes L/L$ in the case where $ L$ is a reductive group and the natural representation $ L:\mathfrak{n}/[\mathfrak{n},\mathfrak{n}]$, where $ \mathfrak{n}$ is the tangent algebra of the group $ N$, is irreducible.


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Additional Information

I. V. Losev
Affiliation: 19–706, 2nd Bagration Per., Minsk 220037, Belarus
Email: ivanlosev@yandex.ru

DOI: https://doi.org/10.1090/S0077-1554-06-00155-5
Published electronically: December 27, 2006
Article copyright: © Copyright 2006 American Mathematical Society

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