Kac, V. G. Some remarks on nilpotent orbits. (English) Zbl 0431.17007 J. Algebra 64, 190-213 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 8 ReviewsCited in 156 Documents MathOverflow Questions: Representations with finitely many nilpotent orbits MSC: 17B45 Lie algebras of linear algebraic groups 15A72 Vector and tensor algebra, theory of invariants 20G05 Representation theory for linear algebraic groups 14L30 Group actions on varieties or schemes (quotients) Keywords:nilpotent element; simple graded Lie algebra; invariant theory; nilpotent orbits; connected linear groups; Kantor functor; isomorphism Citations:Zbl 0043.170; Zbl 0364.22006; Zbl 0391.20035 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Bala, P.; Carter, R. W., Classes of unipotent elements in simple algebraic groups, I, (Proc. Cambridge Philos. Soc., 79 (1976)), 401-425 · Zbl 0364.22006 [2] Dynkin, E. B., Semisimple subalgebras of semisimple Lie algebras, Transl. Amer. Math. Soc., 6, 111-244 (1957) · Zbl 0077.03404 [3] Kac, V. C., Simple irreducible graded Lie algebras of finite growth, Math. USSR-Izv., 2, 1271-1311 (1968) · Zbl 0222.17007 [4] Kac, V. G., Automorphisms of finite order of semisimple Lie algebras, Functional Anal. Appl., 3, 252-254 (1969) · Zbl 0274.17002 [5] Kac, V. G., Concerning the question of description of the orbit space of a linear algebraic group, Uspehi Mat. Nauk., 30, 173-174 (1975), (in Russian) · Zbl 0391.20035 [6] Kac, V. G.; Popov, V. L.; Vinberg, E. B., Sur les groupes linéares algebrique dont l’algebre des invariants est libre, C. R. Acad. Sci. Paris, 283, 875-878 (1976) · Zbl 0343.20023 [7] Kac, V. G., Classification of simpleZ-graded Lie superalgebras and simple Jordan superalgebras, Comm. Algebra, 5, 13, 1375-1400 (1977) · Zbl 0367.17007 [8] Gatti, V.; Viniberghi, E., Spinors of 13-dimensional space, Advances in Math., 30, 137-155 (1978) · Zbl 0429.20043 [9] Kantor, I. L., Some generalizations of Jordan algebras, (Proc. Sem. Vector and tensor Anal., 16 (1972)), 407-499, (in Russian) · Zbl 0272.17001 [10] Kimelfeld, B. N.; Vinberg, E. B., Homogeneous domains in flag manifolds and spherical subgroups of semi-simple Lie groups, Functional Anal. Appl., 12, 3, 12-19 (1978) [11] Kostant, B., The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group, Amer. J. Math., 81, 973-1032 (1959) · Zbl 0099.25603 [12] Popov, A. M., Irreducible semisimple linear groups with finite stabilizers of general position, Functional-Anal. Appl., 91-92 (1978) [13] Popov, V. L., Representations with a free module of covariants, Functional Anal. Appl., 10, 242-244 (1977) · Zbl 0365.20053 [14] Sato, M.; Kimura, T., A classification of irreducible prehomogeneous vector spaces and their relative invariants, Nagoya Math. J., 65, 1-155 (1977) · Zbl 0321.14030 [15] Schwartz, G. W., Representations of simple Lie groups with regular rings of invariants, Invent. Math., 49, 167-191 (1978) · Zbl 0391.20032 [16] Servedio, F. J., Prehomogeneous vector spaces and varieties, Trans. Amer. Math. Soc., 176, 421-444 (1973) · Zbl 0266.20043 [17] Steinberg, R., On the disingularization of the unipotent variety, Invent. Math., 36, 209-224 (1976) · Zbl 0352.20035 [18] Vinberg, E. B.; Onishik, A. L., (Seminar on algebraic groups and Lie groups (1969), Moscow University) [19] Vinberg, E. B., The Weyl group of a graded Lie algebra, Math. USSR-Izv., 10, 463-495 (1976) · Zbl 0371.20041 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.