Publication:
Invariants of solvable rigid Lie algebras up to dimension 8

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http://iopscience.iop.org/0305-4470/35/30/307/pdf/0305-4470_35_30_307.pdf
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Publication Date
2002
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Iop science
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Abstract
The invariants of all complex solvable rigid Lie algebras up to dimension eight are computed. Moreover we show, for rank one solvable algebras, some criteria to deduce to non-existence of non-trivial invariants or the existence of fundamental sets of invariants formed by rational functions of the Casimir invariants of the associated nilradical.
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Álgebra
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1201 Álgebra
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Casimir H 1931 Proc. R. Acad. Amsterdam 34 844 Racah G 1950 Rend. Lincei 8 108 Dixmier J 1974 Alg`ebres enveloppantes (Gauthier-Villard: Paris) Abellanas L and Martinez Alonso L 1975 J. Math. Phys. 16 1580 Ndogmo J C and Winternitz P 1994 J. Phys. A: Math. Gen. 27 405 Ndogmo J C and Winternitz P 1994 J. Phys. A: Math. Gen. 27 2787 Ndogmo J C 2000 J. Phys. A: Math. Gen. 33 2273 Patera J, Sharp R T and Winternitz P 1976 J. Math. Phys. 17 986 Vilela Mendes R 1994 J. Phys. A: Math. Gen. 27 8091 Goze M and Ancochea Bermudez J M 1992 Comm. Algebra 20 875 Goze M and Ancochea Bermudez J M 1999 Proc. Amer. Math. Soc. 127 2611 Nijenhuis A and Richardson J W 1966 Bull. Amer. Math. Soc. 72 1 Richardson J W 1967 Pac. J. Math. 22 339 Malcev A 1945 Izvest. Akad. Nauk. SSR 9 329 Carles R 1984 Ann. Inst. Fourier 34 65 Dickson L E 1924 Ann. Math. 25 294 Rubin J and Winternitz P 1993 J. Phys. A: Math. Gen. 26 1123 Angelopoulos E 1967 C. R. A. S. Paris 264 585 Beltrametti E G and Blasi A 1966 Phys. Lett. 20 62 Seeley C 1988 Seven dimensional nilpotent Lie algebras over the complex number (Ph. Thesis: University of Chicago) Ancochea Bermudez J M and Goze M 2001 J. Algebra 245 68 Vergne M 1970 Bull. Soc. Math. France 98 81 Ancochea Bermudez J M and Campoamor R 2001 Comm. Algebra 29 427 Carles R 1985 Math. Ann. 272 477 Ancochea Bermudez J M and Campoamor R 2001 Alg. Groups Geom. 18 393 Zhu L 1998 Univ. Math. Biq. 15 34
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https://hdl.handle.net/20.500.14352/58589
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