Affine structures on three-step nilpotent Lie algebras
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- by John Scheuneman PDF
- Proc. Amer. Math. Soc. 46 (1974), 451-454 Request permission
Abstract:
As part of the investigation of the parallel between solvable Lie theory and the theory of groups of affine motions, it is proved that every three-step nilpotent Lie algebra admits a faithful representation of a certain special kind. It follows immediately that every three-step nilpotent Lie group which is connected, simply connected, and of dimension $n$ admits a representation as a simply transitive group of affine motions of ${R^n}$.References
- Louis Auslander, The structure of complete locally affine manifolds, Topology 3 (1964), no. suppl, suppl. 1, 131–139. MR 161255, DOI 10.1016/0040-9383(64)90012-6
- John Scheuneman, Examples of compact locally affine spaces, Bull. Amer. Math. Soc. 77 (1971), 589–592. MR 290370, DOI 10.1090/S0002-9904-1971-12764-7
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 46 (1974), 451-454
- MSC: Primary 22E25
- DOI: https://doi.org/10.1090/S0002-9939-1974-0412344-2
- MathSciNet review: 0412344