Homogeneous Lie algebras and expanding automorphisms
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- by R. Warren Johnson PDF
- Proc. Amer. Math. Soc. 48 (1975), 292-296 Request permission
Abstract:
A condition is given which, if satisfied by the spectrum of an automorphism of a Lie algebra, implies that the Lie algebra is homogeneous. In particular, almost all Lie algebras admitting expanding automorphisms are homogeneous.References
- Louis Auslander, An exposition of the structure of solvmanifolds. I. Algebraic theory, Bull. Amer. Math. Soc. 79 (1973), no. 2, 227–261. MR 486307, DOI 10.1090/S0002-9904-1973-13134-9
- Louis Auslander and John Scheuneman, On certain automorphisms of nilpotent Lie groups, Global Analysis (Proc. Sympos. Pure Math., Vol. XIV, Berkeley, Calif., 1968) Amer. Math. Soc., Providence, R.I., 1970, pp. 9–15. MR 0270395
- Joan L. Dyer, A nilpotent Lie algebra with nilpotent automorphism group, Bull. Amer. Math. Soc. 76 (1970), 52–56. MR 249544, DOI 10.1090/S0002-9904-1970-12364-3
- N. Jacobson, A note on automorphisms and derivations of Lie algebras, Proc. Amer. Math. Soc. 6 (1955), 281–283. MR 68532, DOI 10.1090/S0002-9939-1955-0068532-9
- Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0143793
- G. Leger, Derivations of Lie algebras. III, Duke Math. J. 30 (1963), 637–645. MR 159848
- G. D. Mostow, Factor spaces of solvable groups, Ann. of Math. (2) 60 (1954), 1–27. MR 61611, DOI 10.2307/1969700
- Jean-Pierre Serre, Lie algebras and Lie groups, W. A. Benjamin, Inc., New York-Amsterdam, 1965. Lectures given at Harvard University, 1964. MR 0218496
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 48 (1975), 292-296
- MSC: Primary 17B40
- DOI: https://doi.org/10.1090/S0002-9939-1975-0374217-4
- MathSciNet review: 0374217