The jacobian modules of a representation of a Lie algebra and geometry of commuting varieties

Dmitrii I. Panyushev

Compositio Mathematica (1994)

  • Volume: 94, Issue: 2, page 181-199
  • ISSN: 0010-437X

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Panyushev, Dmitrii I.. "The jacobian modules of a representation of a Lie algebra and geometry of commuting varieties." Compositio Mathematica 94.2 (1994): 181-199. <http://eudml.org/doc/90333>.

@article{Panyushev1994,
author = {Panyushev, Dmitrii I.},
journal = {Compositio Mathematica},
keywords = {reductive group action; commuting variety; Jacobian module; module of covariants; open problems},
language = {eng},
number = {2},
pages = {181-199},
publisher = {Kluwer Academic Publishers},
title = {The jacobian modules of a representation of a Lie algebra and geometry of commuting varieties},
url = {http://eudml.org/doc/90333},
volume = {94},
year = {1994},
}

TY - JOUR
AU - Panyushev, Dmitrii I.
TI - The jacobian modules of a representation of a Lie algebra and geometry of commuting varieties
JO - Compositio Mathematica
PY - 1994
PB - Kluwer Academic Publishers
VL - 94
IS - 2
SP - 181
EP - 199
LA - eng
KW - reductive group action; commuting variety; Jacobian module; module of covariants; open problems
UR - http://eudml.org/doc/90333
ER -

References

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  2. [BPV] J.R. Brennan, M.V. Pinto and W.V. Vasconcelos, The Jacobian module of a Lie algebra, Trans. Amer. Math. Soc.321 (1990), 183-196. Zbl0712.17004MR958883
  3. [HSV] J. Herzog, A. Simis and W.V. Vasconcelos, On the arithmetic and homology of algebras of linear type, Trans. Amer. Math. Soc.283 (1984), 661-683. Zbl0541.13005MR737891
  4. [Kac] V.G. Kac, Some remarks on nilpotent orbits, J. Algebra64 (1980), 190-213. Zbl0431.17007MR575790
  5. [KR] B. Kostant and S. Rallis, Orbits and representations associated with symmetric spaces, Amer. J. Math.93 (1971), 753-809. Zbl0224.22013MR311837
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  7. [K] H. Kraft, Geometrische Methoden in der Invariantentheorie, Aspekte der Mathematik D1, Vieweg-Verlag, Braunschweig1984. Zbl0669.14003MR768181
  8. [LR] D. Luna and R.W. Richardson, A generalization of the Chevalley restriction theorem, Duke Math. J.46 (1979), 487-496. Zbl0444.14010MR544240
  9. [Pa] D.I. Panyushev, On orbit spaces of finite and connected linear groups, Math. USSR-Izv.20 (1983), 97-101. Zbl0517.20019MR643895
  10. [P] V.S. Pyasetskii, Linear Lie groups acting with finitely many orbits, Functional Anal. Appl.9 (1975), 351-353. Zbl0326.22004
  11. [Ri] R.W. Richardson, Commuting varieties of semisimple Lie algebras and algebraic groups, Compositio Math.38 (1979), 311-327. Zbl0409.17006MR535074
  12. [SV] A. Simis and W.V. Vasconcelos, Krull dimension and integrality of symmetric algebras, Manuscripta Math.61 (1988), 63-78. Zbl0687.13010MR939141
  13. [Vi1] E.B. Vinberg, The Weyl group of a graded Lie algebra, Math. USSR-Izv. 10 (1976), 463-495. Zbl0371.20041MR430168
  14. [Vi2] E.B. Vinberg, Complexity of actions of reductive groups, Functional. Anal. Appl.20 (1986), 1-11. Zbl0601.14038MR831043
  15. [VP] E.B. Vinberg and V.L. Popov, "Invariant theory", in: Contemporary problems in Math. Fundamental aspects, v. 55. Moscow, VINITI, 1989 (Russian). (English translation in: Encyclopaedia of Math. Sci., v. 55, Berlin-Springer, 1994.) Zbl0789.14008MR1100485

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