Abstract
The new notion of (G-graded contraction of Lie algebras is briefly surveyed. As physical applications, our results on Z2 × Z2-graded contractions of several Lie algebras commonly used in physics are presented, based on common papers with M. de Montigny, J. Patera, and P. Trávníček.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H. Bacry and J.-M. Levy-Leblond, Possible kinematics, J. Math. Phys. 9 (1968), 1605–1614.
H. Bacry and J. Nuyts, Classification of ten-dimensional kinematical groups with space isotropy, J. Math. Phys. 27 (1986), 2455–2457.
H.D. Doebner and O. Melsheimer, On a class of generalized group contractions, N. Cimento A 49 (1967), 306–311.
M. Gerstenhaber, On the deformation of rings and algebras, Ann. Math. 79 (1964), 59–103.
R. Gilmore, Lie groups, Lie algebras and some of their applications, Chapter 10, J. Wiley&Sons, New York, 1974.
E. Inönü and E.P. Wigner, On the contraction of groups and their representations, Proc. Nat. Acad. Sci. US 9 (1953), 510–524; On a particular type of convergence to a singular matrix, ibid. 40 (1954), 119-121.
M. Lévy-Nahas, Monique deformation and contraction of Lie algebras, J. Math. Phys. 8 (1967), 1211–1222.
M. de Montigny and J. Patera, Discrete and continuous graded contractions of Lie algebras and superalgebras, J. Phys. A 24 (1991), 525–549.
M. de Montigny, J. Patera, and J. Tolar, Graded contractions and kinematical groups of spacetime, J. Math. Phys. 35 (1994), 405–425.
R.V. Moody and J. Patera, Discrete and continuous graded contractions of representations of Lie algebras, J. Phys. A 24 (1991), 2227–2258.
J. Patera, Graded contractions of Lie algebras, their representations, and tensor products, Group Theory in Physics (Cocoyoc, 1991), AIP Conf. Proa, Amer. Inst. Phys., Vol. 266, New York, 1992, pp. 46–54.
G. Rosensteel and D. J. Rowe, On the algebraic formulation of collective models. III. The symplectic shell model of collective motion, Ann. Phys. 2 (1980), 343–369.
E.J. Saletan, Contraction of Lie groups, J. Math. Phys. 2 (1961), 1–21.
I.E. Segal, A class of operator algebras which are determined by groups, Duke Math. J. 18 (1951), 221–265.
I.T. Todorov, Infinite-dimensional Lie algebras in conformai QFT models, Lecture Notes in Physics, vol. 261, Springer-Verlag, Berlin, 1986, pp. 387–443.
J. Tolar and P. Trávnícek, Graded contractions and the conformai group of Minkowski spacetime, J. Math. Phys. 36 (1995), 4489–4506.
J. Tolar and P. Trávnícek, Graded contractions of symplectic Lie algebras in collective models, J. Math. Phys. 38 (1997), 49–56.
E.C. Zeeman, Causality implies Lorentz group, J. Math. Phys. 5 (1964), 490–493.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media New York
About this chapter
Cite this chapter
Tolar, J. (2001). Graded Contractions of Lie Algebras of Physical Interest. In: Saint-Aubin, Y., Vinet, L. (eds) Algebraic Methods in Physics. CRM Series in Mathematical Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0119-6_17
Download citation
DOI: https://doi.org/10.1007/978-1-4613-0119-6_17
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6528-3
Online ISBN: 978-1-4613-0119-6
eBook Packages: Springer Book Archive