Automorphisms compatible with group actions
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- by Michael A. Gauger PDF
- Proc. Amer. Math. Soc. 48 (1975), 251-254 Request permission
Abstract:
Let $A$ be a group of bijections of the set $\mathcal {V}$ and let $G$ be a subgroup of $A$. Our purpose here is to introduce several other subgroups of $A$ consisting of bijections compatible with the $G$-orbit structure on $\mathcal {V}$ and to investigate these groups when $\mathcal {V}$ is the Grassmann variety of all $p$-dimensional subspaces of a vector space $V$ and $G$ is a group of automorphisms of the Grassmannian induced by a group of linear transformations on $V$.References
- Armand Borel, Linear algebraic groups, W. A. Benjamin, Inc., New York-Amsterdam, 1969. Notes taken by Hyman Bass. MR 0251042
- Michael A. Gauger, Duality theories for metabelian Lie algebras, Trans. Amer. Math. Soc. 187 (1974), 89–102. MR 342576, DOI 10.1090/S0002-9947-1974-0342576-8
- Michael A. Gauger, Duality theories for metabelian Lie algebras. II, Trans. Amer. Math. Soc. 203 (1975), 67–75. MR 360728, DOI 10.1090/S0002-9947-1975-0360728-9
- R. Westwick, Linear transformations on Grassman spaces, Pacific J. Math. 14 (1964), 1123–1127. MR 167493
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 48 (1975), 251-254
- MSC: Primary 14M15; Secondary 57E25
- DOI: https://doi.org/10.1090/S0002-9939-1975-0369378-7
- MathSciNet review: 0369378