| Title:
|
Contractions of Lie algebras and algebraic groups (English) |
| Author:
|
Burde, Dietrich |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
43 |
| Issue:
|
5 |
| Year:
|
2007 |
| Pages:
|
321-332 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Degenerations, contractions and deformations of various algebraic structures play an important role in mathematics and physics. There are many different definitions and special cases of these notions. We try to give a general definition which unifies these notions and shows the connections among them. Here we focus on contractions of Lie algebras and algebraic groups. (English) |
| Keyword:
|
contractions |
| Keyword:
|
Lie algebras |
| Keyword:
|
affine algebraic groups |
| Keyword:
|
affine group schemes |
| MSC:
|
14L15 |
| MSC:
|
14Lxx |
| MSC:
|
17B81 |
| MSC:
|
17B99 |
| MSC:
|
17Bxx |
| MSC:
|
20G99 |
| MSC:
|
20Gxx |
| MSC:
|
81R05 |
| idZBL:
|
Zbl 1199.14016 |
| idMR:
|
MR2381781 |
| . |
| Date available:
|
2008-06-06T22:51:50Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108077 |
| . |
| Reference:
|
[1] Agaoka Y.: An algorithm to determine the isomorphism classes of 4-dimensional complex Lie algebras.Linear Algebra Appl. 345 (2002), 85–118. Zbl 0998.17002, MR 1883269 |
| Reference:
|
[2] Borel A.: Lienar Algebraic Groups.Graduate Texts in Mathematics, 126, Springer-Verlag, New York (1991), 1–288. MR 1102012 |
| Reference:
|
[3] Burde D.: Degenerations of nilpotent Lie algebras.J. Lie Theory 9 (1999), 193–202. Zbl 1063.17009, MR 1679999 |
| Reference:
|
[4] Burde D., Steinhoff C.: Classification of orbit closures of $4$–dimensional complex Lie algebras.J. Algebra 214 (1999), 729–739. Zbl 0932.17005, MR 1680532 |
| Reference:
|
[5] Burde D.: Degenerations of $7$-dimensional nilpotent Lie Algebras.Commun. Algebra 33, No. 4 (2005), 1259–1277. Zbl 1126.17011, MR 2136700 |
| Reference:
|
[6] Carles R., Diakité Y.: Sur les variétés d’algèbres de Lie de dimension $\le 7$.J. Algebra 91 (1984), 53–63. Zbl 0546.17006, MR 0765770 |
| Reference:
|
[7] Daboul C.: Deformationen und Degenerationen von Lie Algebren und Lie Gruppen.Dissertation (1999), Universität Hamburg. |
| Reference:
|
[8] Gerstenhaber M., Schack S. D.: Relative Hochschild cohomology, rigid Lie algebras and the Bockstein.J. Pure Appl. Algebra 43, No. 1 (1986), 53–74. MR 0862872 |
| Reference:
|
[9] Grunewald F., O’Halloran J.: A characterization of orbit closure and applications.J. Algebra 116 (1988), 163–175. Zbl 0646.17002, MR 0944153 |
| Reference:
|
[10] Hartshorne R.: Algebraic Geometry.Graduate Texts in Mathematics, 52 (1977). Zbl 0367.14001, MR 0463157 |
| Reference:
|
[11] Inönü E., Wigner E. P.: On the contraction of groups and their representations.Proc. Natl. Acad. Sciences USA 39 (1953), 510–524. Zbl 0050.02601, MR 0055352 |
| Reference:
|
[12] Lauret J.: Degenerations of Lie algebras and Geometry of Lie groups.Differ. Geom. Appl. 18, No. 2 (2003), 177–194. MR 1958155 |
| Reference:
|
[13] Nesterenko M., Popovych R.: Contractions of low-dimensional Lie algebras.J. Math. Phys. 47 (2006), no. 12, 123515, 45 pp. arXiv:math-ph/0608018 (2006). Zbl 1112.17007, MR 2285164 |
| Reference:
|
[14] Segal I. E.: A class of operator algebras determined by groups.Duke Math. J. 18 (1951), 221–265. MR 0045133 |
| . |
