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Determinantal formulae for the Casimir operators of inhomogeneous Lie algebras

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2006
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IOP Publishing
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Contractions of Lie algebras are combined with the classical matrix method of Gel’fand to obtain matrix formulae for the Casimir operators of inhomogeneous Lie algebras. The method is presented for the inhomogeneous pseudounitary Lie algebras Iu(p, q). This procedure is extended to contractions of Iu(p, q) isomorphic to an extension by a derivation of the inhomogeneous special pseudo-unitary Lie algebras Isu(p − 1, q), providing an additional analytical method to obtain their invariants. Further, matrix formulae for the invariants of other inhomogeneous Lie algebras are presented.
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Gilmore R, Feng D H, Vallieres M and Wood J L 1983 Phys. Rev. Letters C28 903 Perjés Z 1979 Phys. Rev. D20 1857 Demichev A P, Nelipa N F and Chai’chian M 1983 Comm. Math. Phys. 90 353 Herranz F J, Santander M 1997 J. Phys. A: Math. Gen. 30 5411 Pecina Cruz J N 1994 J. Math. Phys. 35 3146 Campoamor-Stursberg R 2003 J. Phys. A: Math. Gen. 36 1357 Gel’fand I M 1950 Mat. Sbornik 26 112 Herranz F J, Perez Bueno J C and Santander M 1998 J. Phys. A: Math. Gen. 31 5327 Lykhmus Ya Kh 1969 Predel’nye (szhatye) gruppy Li Tartu Rosen J J. Math. Phys. 9 1305 Beltrametti E G and Blasi A 1966 Phys. Lett. 20 62 Campoamor-Stursberg R 2003 Acta Phys. Polonica 34 3901; 35 2059. Campoamor-Stursberg R 2003 Phys. Lett. A 312 211 Racah G 1951 Group Theory and Spectroscopy (Princeton Univ. Press, N. J.) Perelomov A M and Popov V S 1967 Yad. Fiz 3 924 Campoamor-Stursberg R 2004 Phys. Lett. A 327 138 Abellanas L and Martínez Alonso L 1975 J. Math. Phys. 16 1580 Gilmore R 1974 Lie groups, Lie algebras and some of its applications (New York: Wiley)
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