# Contractions of Lie algebras and algebraic groups

Archivum Mathematicum (2007)

- Volume: 043, Issue: 5, page 321-332
- ISSN: 0044-8753

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topBurde, Dietrich. "Contractions of Lie algebras and algebraic groups." Archivum Mathematicum 043.5 (2007): 321-332. <http://eudml.org/doc/250177>.

@article{Burde2007,

abstract = {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.},

author = {Burde, Dietrich},

journal = {Archivum Mathematicum},

keywords = {contractions; Lie algebras; affine algebraic groups; affine group schemes; contractions; Lie algebras; affine algebraic groups; affine group schemes},

language = {eng},

number = {5},

pages = {321-332},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Contractions of Lie algebras and algebraic groups},

url = {http://eudml.org/doc/250177},

volume = {043},

year = {2007},

}

TY - JOUR

AU - Burde, Dietrich

TI - Contractions of Lie algebras and algebraic groups

JO - Archivum Mathematicum

PY - 2007

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 043

IS - 5

SP - 321

EP - 332

AB - 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.

LA - eng

KW - contractions; Lie algebras; affine algebraic groups; affine group schemes; contractions; Lie algebras; affine algebraic groups; affine group schemes

UR - http://eudml.org/doc/250177

ER -

## References

top- Agaoka Y., An algorithm to determine the isomorphism classes of 4-dimensional complex Lie algebras, Linear Algebra Appl. 345 (2002), 85–118. Zbl0998.17002MR1883269
- Borel A., Lienar Algebraic Groups, Graduate Texts in Mathematics, 126, Springer-Verlag, New York (1991), 1–288. (1991) MR1102012
- Burde D., Degenerations of nilpotent Lie algebras, J. Lie Theory 9 (1999), 193–202. (1999) Zbl1063.17009MR1679999
- Burde D., Steinhoff C., Classification of orbit closures of $4$–dimensional complex Lie algebras, J. Algebra 214 (1999), 729–739. (1999) Zbl0932.17005MR1680532
- Burde D., Degenerations of $7$-dimensional nilpotent Lie Algebras, Commun. Algebra 33, No. 4 (2005), 1259–1277. Zbl1126.17011MR2136700
- Carles R., Diakité Y., Sur les variétés d’algèbres de Lie de dimension $\le 7$, J. Algebra 91 (1984), 53–63. (1984) Zbl0546.17006MR0765770
- Daboul C., Deformationen und Degenerationen von Lie Algebren und Lie Gruppen, Dissertation (1999), Universität Hamburg. (1999)
- Gerstenhaber M., Schack S. D., Relative Hochschild cohomology, rigid Lie algebras and the Bockstein, J. Pure Appl. Algebra 43, No. 1 (1986), 53–74. (1986) MR0862872
- Grunewald F., O’Halloran J., A characterization of orbit closure and applications, J. Algebra 116 (1988), 163–175. (1988) Zbl0646.17002MR0944153
- Hartshorne R., Algebraic Geometry, Graduate Texts in Mathematics, 52 (1977). (1977) Zbl0367.14001MR0463157
- Inönü E., Wigner E. P., On the contraction of groups and their representations, Proc. Natl. Acad. Sciences USA 39 (1953), 510–524. (1953) Zbl0050.02601MR0055352
- Lauret J., Degenerations of Lie algebras and Geometry of Lie groups, Differ. Geom. Appl. 18, No. 2 (2003), 177–194. (194.) MR1958155
- 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). Zbl1112.17007MR2285164
- Segal I. E., A class of operator algebras determined by groups, Duke Math. J. 18 (1951), 221–265. (1951) MR0045133

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