Deformation of Lie algebras and Lie algebras of deformations

Harald Bjar; Olav Arnfinn Laudal

Compositio Mathematica (1990)

  • Volume: 75, Issue: 1, page 69-111
  • ISSN: 0010-437X

How to cite

top

Bjar, Harald, and Laudal, Olav Arnfinn. "Deformation of Lie algebras and Lie algebras of deformations." Compositio Mathematica 75.1 (1990): 69-111. <http://eudml.org/doc/90029>.

@article{Bjar1990,
author = {Bjar, Harald, Laudal, Olav Arnfinn},
journal = {Compositio Mathematica},
keywords = {miniversal deformation; deformation of the Lie algebra; quasihomogeneous isolated plane curve singularity},
language = {eng},
number = {1},
pages = {69-111},
publisher = {Kluwer Academic Publishers},
title = {Deformation of Lie algebras and Lie algebras of deformations},
url = {http://eudml.org/doc/90029},
volume = {75},
year = {1990},
}

TY - JOUR
AU - Bjar, Harald
AU - Laudal, Olav Arnfinn
TI - Deformation of Lie algebras and Lie algebras of deformations
JO - Compositio Mathematica
PY - 1990
PB - Kluwer Academic Publishers
VL - 75
IS - 1
SP - 69
EP - 111
LA - eng
KW - miniversal deformation; deformation of the Lie algebra; quasihomogeneous isolated plane curve singularity
UR - http://eudml.org/doc/90029
ER -

References

top
  1. [B-L] Bjar, H. and Laudal, O.A., Deformation of Lie algebras and Lie algebras of deformations. Application to the study of hypersurface singularities. Preprint No. 3 1987, University of Oslo. 
  2. [C] Cartier, P., Effacement dans la cohomologie des algebres de Lie. Séminaire Bourbaki, May 1955. Zbl0116.02402
  3. [C-D] Carles, R. and Diakité, Y., Sur les varietés d'algebres de Lie de dimension ≤ 7. J. Algebra91 (1984) pp. 53-63. Zbl0546.17006
  4. [Ca-E] Cartan, H. and Eilenberg, S., Homological Algebra. Princeton Mathematical Series no. 19. Zbl0075.24305
  5. [Ch-E] Chevalley, C. and Eilenberg, S., Cohomology theory of Lie groups and Lie algebras. Trans. Amer. Math. Soc.63 (1948) pp. 85-124. Zbl0031.24803MR24908
  6. [E] Elkik, R., Solutions d'équations à coeffisients dans un anneau Hensélien. Ann. scient. Ec. Norm. Sup.4 e série, t. 6 (1973), pp. 553-604. Zbl0327.14001MR345966
  7. [Fi] Fialovski, A., Deformations of Lie algebras. Math. USSR Sbornik, vol. 55 (1985), pp. 467-473. Zbl0597.17010
  8. [J] Jacobson, N., Lie algebras. Tracts in Mathematics No. 10, Interscience Publishers1962. Zbl0121.27504MR143793
  9. [K-N] Kirillov, A.A. and Neretin, Yu.A., The variety An of n-dimensional Lie algebra structures. Am. Math. Soc. Transl. (2) Vol. 137 (1987) pp. 21-30. Zbl0646.17014MR902292
  10. [La 1] Laudal, O.A., Formal moduli of algebraic structures. Lecture Notes in Mathematics, Springer Verlag, No. 754 (1979). Zbl0438.14007MR551624
  11. [La-M-Pf] Laudal, O.A., Martin, B. and Pfister, G., Moduli of plane curve singularities with C*-action. Banach Center Publ., Vol. 20, PWN-Polish Scientific Publishers, Warsaw1988. Zbl0691.14018MR1101844
  12. [La-Pf] Laudal, O.A. and Pfister, G., Local moduli and singularities. Lecture Notes in Mathematics, Springer Verlag, No. 1310 (1988). Zbl0657.14005MR950171
  13. [Ma-Y] Mather, J.N. and Yau, S.S.-T., Classification of isolated hypersurface singularities by their moduli algebras. Invent. math.69 (1982), pp. 243-251. Zbl0499.32008MR674404
  14. [Mo] Mori, M., On the three-dimensional cohomology group of Lie algebras. J. Math. Soc. of Japan, Vol. 5 (July 1953). Zbl0051.02304MR57854
  15. [Mos] Mostow, G.D., Fully reducible subgroups of algebraic groups. Am. J. Math.78, pp. 200-221 (1956). Zbl0073.01603MR92928
  16. [N] Neretin, Yu.A., An estimate for the number of parameters defining an n-dimensional algebra. Izv. Akad. Nauk. SSSR51 No. 2 (1987) pp. 306-318, (Math. USSR Izv.30 No. 2 (1988) pp. 283-294). Zbl0641.17012MR896999
  17. [Ra] Rauch, G., Effacement et déformation. Ann. Inst. Fourier, Grenoble, 22, 1 (1972), pp. 239-269. Zbl0219.17006MR335587
  18. [Ri] Rim, D.S., Deformation of transitive Lie algebras. Ann. of Math. (1966), pp. 339-357. Zbl0136.43104MR199315
  19. [San] Santharoubane, L.J., Kac-Moody Lie algebras and the universal element for the category of nilpotent Lie algebras. Math. Ann.263, pp. 365-370 (1983). Zbl0495.17012MR704300
  20. [V 1] Vergne, M., Variétes des algèbres de Lie nilpotentes. Thèse, Université de Paris (1966). 
  21. [V 2] Vergne, M., Cohomologie des algèbres de Lie nilpotentes. Bull. Soc. Math. de France, T. 98 (1970), pp. 81-116. Zbl0244.17011MR289609
  22. [V 3] Vergne, M., Réductibilité de la varieté des algèbres de Lie nilpotentes. C.R. Acad. Sc. Paris, t. 263, Ser. A (1966), pp. 4-6. Zbl0145.25902MR199237
  23. [Y] Yau, Stephen S.-T., Solvable Lie algebras and generalized Cartan Matrices arising from isolated singularities. Math. Zeitschrift191 (1986), pp. 489-506. Zbl0589.17012MR832806

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.