On rational invariants of the group $E_6$
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- by A. V. Iltyakov PDF
- Proc. Amer. Math. Soc. 124 (1996), 3637-3640 Request permission
Abstract:
We prove rationality of the field of invariants in several variables of a minimal irreducible representation of a simple algebraic group of type $E_6$ over an algebraically closed field of characteristic zero.References
- Saunders MacLane, Steinitz field towers for modular fields, Trans. Amer. Math. Soc. 46 (1939), 23β45. MR 17, DOI 10.1090/S0002-9947-1939-0000017-3
- Igor V. Dolgachev, Rationality of fields of invariants, Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985) Proc. Sympos. Pure Math., vol. 46, Amer. Math. Soc., Providence, RI, 1987, pp.Β 3β16. MR 927970
- A.V. Iltyakov and I.P. Shestakov, Invariants of $F_4$ and center of the Albert algebra, J. Algebra, 179 (1996), pp. 838β851.
- Nathan Jacobson, Structure and representations of Jordan algebras, American Mathematical Society Colloquium Publications, Vol. XXXIX, American Mathematical Society, Providence, R.I., 1968. MR 0251099, DOI 10.1090/coll/039
- N. Jacobson, Some groups of transformations defined by Jordan algebras. III, J. Reine Angew. Math. 207 (1961), 61β85. MR 159850, DOI 10.1515/crll.1961.207.61
- Kevin McCrimmon, The Freudenthal-Springer-Tits constructions revisited, Trans. Amer. Math. Soc. 148 (1970), 293β314. MR 271181, DOI 10.1090/S0002-9947-1970-0271181-3
- Γ. B. Vinberg and V. L. Popov, Invariant theory, Algebraic geometry, 4 (Russian), Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1989, pp.Β 137β314, 315 (Russian). MR 1100485
- David J. Saltman, Invariant fields of linear groups and division algebras, Perspectives in ring theory (Antwerp, 1987) NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., vol. 233, Kluwer Acad. Publ., Dordrecht, 1988, pp.Β 279β297. MR 1048416
Additional Information
- A. V. Iltyakov
- Affiliation: Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Novosibirsk, 630090, Russia
- Address at time of publication: School of Mathematics and Statistics, University of Sydney, 2006 New South Wales, Australia
- Received by editor(s): June 8, 1995
- Additional Notes: During 1993/94 a Becario de FICYT at the University of Oviedo, Asturias, Spain
- Communicated by: Eric Friedlander
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 3637-3640
- MSC (1991): Primary 20G15; Secondary 17C20
- DOI: https://doi.org/10.1090/S0002-9939-96-03584-8
- MathSciNet review: 1350947