Commuting varieties of semisimple Lie algebras and algebraic groups

R. W. Richardson

Compositio Mathematica (1979)

  • Volume: 38, Issue: 3, page 311-327
  • ISSN: 0010-437X

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Richardson, R. W.. "Commuting varieties of semisimple Lie algebras and algebraic groups." Compositio Mathematica 38.3 (1979): 311-327. <http://eudml.org/doc/89407>.

@article{Richardson1979,
author = {Richardson, R. W.},
journal = {Compositio Mathematica},
keywords = {Semisimple Lie Algebras; Irreducible Algebraic Variety; Reductive Lie Algebras; Simply Connected Semisimple Algebraic Groups; Cartan Subalgebra},
language = {eng},
number = {3},
pages = {311-327},
publisher = {Sijthoff et Noordhoff International Publishers},
title = {Commuting varieties of semisimple Lie algebras and algebraic groups},
url = {http://eudml.org/doc/89407},
volume = {38},
year = {1979},
}

TY - JOUR
AU - Richardson, R. W.
TI - Commuting varieties of semisimple Lie algebras and algebraic groups
JO - Compositio Mathematica
PY - 1979
PB - Sijthoff et Noordhoff International Publishers
VL - 38
IS - 3
SP - 311
EP - 327
LA - eng
KW - Semisimple Lie Algebras; Irreducible Algebraic Variety; Reductive Lie Algebras; Simply Connected Semisimple Algebraic Groups; Cartan Subalgebra
UR - http://eudml.org/doc/89407
ER -

References

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  1. [1] P. Bala and R. Carter: Unipotent elements in semisimple algebraic groups. I. Math. Proc. Cambridge Philos. Soc.79 (1976) 401-425. Zbl0364.22006MR417306
  2. [2] A. Borel: Linear Algebraic Groups. Benjamin, New York, 1969. Zbl0186.33201MR251042
  3. [3] A. Borel and J.-P. Serre: Théorèmes de finitude en cohomologie galoisienne. Comment. Math. Helv.39 (1964) 111-164. Zbl0143.05901MR181643
  4. [4] N. Bourbaki: Éléments de mathematique; Groupes et algèbres de Lie, Chap. 7 et 8. Hermann, Paris, 1975. Zbl0505.22006MR453824
  5. [5] J. Dixmier: Polarisations dans les algebras de Lie semi-simple complexes. Bull. Sci. Math.99 (1975) 45-63. Zbl0314.17009MR435165
  6. [6] M. Gerstenhaber: On dominance and varieties of commuting matrices. Ann. of Math. (2) 73 (1961) 324-348. Zbl0168.28201MR132079
  7. [7] D. Johnston and R. Richardson: Conjugacy classes in parabolic subgroups of semisimple algebraic groups, II. Bull. London Math. Soc.9 (1977) 245-250. Zbl0375.22008MR480766
  8. [8] B. Kostant: On the conjugacy of real Cartan subalgebras. I. Proc. Nat. Acad. Sci. USA41 (1955) 967-970. Zbl0065.26901MR73928
  9. [9] R. Richardson: Deformations of Lie subgroups and the variation of isotropy supgroups. Acta Math.129 (1972) 35-73. Zbl0242.22020MR299723
  10. [10] R. Richardson: Conjugacy classes of parabolic subgroups in semisimple algebraic groups. Bull. London Math. Soc.6 (1974) 21-24. Zbl0287.20036MR330311
  11. [11] T. Springer and R. Steinberg: Conjugacy classes, in Seminar in Algebraic Groups and Related Finite Groups, ed. by A. Borel et al., Lecture Notes in Mathematics131, Springer-Verlag, Berlin-Heidelberg-New York, 1970. Zbl0249.20024MR268192

Citations in EuDML Documents

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  1. Oksana Yakimova, Surprising properties of centralisers in classical Lie algebras
  2. Jean-Yves Charbonnel, Propriétés (Q) et (C). Variété commutante
  3. Dmitrii I. Panyushev, The jacobian modules of a representation of a Lie algebra and geometry of commuting varieties
  4. Michaël Bulois, Composantes irréductibles de la variété commutante nilpotente d’une algèbre de Lie symétrique semi-simple
  5. T. Levasseur, J. T. Stafford, The kernel of an homomorphism of Harish-Chandra

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