Contractions of Lie algebras and algebraic groups
Archivum mathematicum, Tome 43 (2007) no. 5, pp. 321-332 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 14L15, 14Lxx, 17B81, 17B99, 17Bxx, 20G99, 20Gxx, 81R05
Keywords: contractions; Lie algebras; affine algebraic groups; affine group schemes
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Burde, Dietrich. Contractions of Lie algebras and algebraic groups. Archivum mathematicum, Tome 43 (2007) no. 5, pp. 321-332. http://geodesic.mathdoc.fr/item/ARM_2007_43_5_a2/

[1] Agaoka Y.: An algorithm to determine the isomorphism classes of 4-dimensional complex Lie algebras. Linear Algebra Appl. 345 (2002), 85–118. | MR | Zbl

[2] Borel A.: Lienar Algebraic Groups. Graduate Texts in Mathematics, 126, Springer-Verlag, New York (1991), 1–288. | MR

[3] Burde D.: Degenerations of nilpotent Lie algebras. J. Lie Theory 9 (1999), 193–202. | MR | Zbl

[4] Burde D., Steinhoff C.: Classification of orbit closures of $4$–dimensional complex Lie algebras. J. Algebra 214 (1999), 729–739. | MR | Zbl

[5] Burde D.: Degenerations of $7$-dimensional nilpotent Lie Algebras. Commun. Algebra 33, No. 4 (2005), 1259–1277. | MR | Zbl

[6] Carles R., Diakité Y.: Sur les variétés d’algèbres de Lie de dimension $\le 7$. J. Algebra 91 (1984), 53–63. | MR | Zbl

[7] Daboul C.: Deformationen und Degenerationen von Lie Algebren und Lie Gruppen. Dissertation (1999), Universität Hamburg.

[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

[9] Grunewald F., O’Halloran J.: A characterization of orbit closure and applications. J. Algebra 116 (1988), 163–175. | MR | Zbl

[10] Hartshorne R.: Algebraic Geometry. Graduate Texts in Mathematics, 52 (1977). | MR | Zbl

[11] Inönü E., Wigner E. P.: On the contraction of groups and their representations. Proc. Natl. Acad. Sciences USA 39 (1953), 510–524. | MR | Zbl

[12] Lauret J.: Degenerations of Lie algebras and Geometry of Lie groups. Differ. Geom. Appl. 18, No. 2 (2003), 177–194. | MR

[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). | MR | Zbl

[14] Segal I. E.: A class of operator algebras determined by groups. Duke Math. J. 18 (1951), 221–265. | MR