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.
@article{108077, author = {Dietrich Burde}, title = {Contractions of Lie algebras and algebraic groups}, journal = {Archivum Mathematicum}, volume = {043}, year = {2007}, pages = {321-332}, zbl = {1199.14016}, mrnumber = {2381781}, language = {en}, url = {http://dml.mathdoc.fr/item/108077} }
Burde, Dietrich. Contractions of Lie algebras and algebraic groups. Archivum Mathematicum, Tome 043 (2007) pp. 321-332. http://gdmltest.u-ga.fr/item/108077/
An algorithm to determine the isomorphism classes of 4-dimensional complex Lie algebras, Linear Algebra Appl. 345 (2002), 85–118. | MR 1883269 | Zbl 0998.17002
Lienar Algebraic Groups, Graduate Texts in Mathematics, 126, Springer-Verlag, New York (1991), 1–288. (1991) | MR 1102012
Degenerations of nilpotent Lie algebras, J. Lie Theory 9 (1999), 193–202. (1999) | MR 1679999 | Zbl 1063.17009
Classification of orbit closures of $4$–dimensional complex Lie algebras, J. Algebra 214 (1999), 729–739. (1999) | MR 1680532 | Zbl 0932.17005
Degenerations of $7$-dimensional nilpotent Lie Algebras, Commun. Algebra 33, No. 4 (2005), 1259–1277. | MR 2136700 | Zbl 1126.17011
Sur les variétés d’algèbres de Lie de dimension $\le 7$, J. Algebra 91 (1984), 53–63. (1984) | MR 0765770 | Zbl 0546.17006
Deformationen und Degenerationen von Lie Algebren und Lie Gruppen, Dissertation (1999), Universität Hamburg. (1999)
Relative Hochschild cohomology, rigid Lie algebras and the Bockstein, J. Pure Appl. Algebra 43, No. 1 (1986), 53–74. (1986) | MR 0862872
A characterization of orbit closure and applications, J. Algebra 116 (1988), 163–175. (1988) | MR 0944153 | Zbl 0646.17002
Algebraic Geometry, Graduate Texts in Mathematics, 52 (1977). (1977) | MR 0463157 | Zbl 0367.14001
On the contraction of groups and their representations, Proc. Natl. Acad. Sciences USA 39 (1953), 510–524. (1953) | MR 0055352 | Zbl 0050.02601
Degenerations of Lie algebras and Geometry of Lie groups, Differ. Geom. Appl. 18, No. 2 (2003), 177–194. (194.) | MR 1958155
Contractions of low-dimensional Lie algebras, J. Math. Phys. 47 (2006), no. 12, 123515, 45 pp. arXiv:math-ph/0608018 (2006). | MR 2285164 | Zbl 1112.17007
A class of operator algebras determined by groups, Duke Math. J. 18 (1951), 221–265. (1951) | MR 0045133