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1997 | 40 | 1 | 159-170

Tytuł artykułu

On the classification of 3-dimensional coloured Lie algebras

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
In this paper, complex 3-dimensional Γ-graded ε-skew-symmetric and complex 3-dimensional Γ-graded ε-Lie algebras with either 1-dimensional or zero homogeneous components are classified up to isomorphism.

Słowa kluczowe

Rocznik

Tom

40

Numer

1

Strony

159-170

Opis fizyczny

Daty

wydano
1997

Twórcy

  • Department of Mathematics, Royal Institute of Technology, S-10044 Stockholm, Sweden

Bibliografia

  • [1] V. K. Agrawala, Invariants of generalized Lie algebras, Hadronic J. 4 (1981), 444-496.
  • [2] N. Backhouse, A classification of four-dimensional Lie superalgebras, J. Math. Phys. 19, 11 (1978), 2400-2402.
  • [3] Yu. A. Bahturin, A. A. Mikhalev, V. M. Petrogradsky and M. V. Zaicev, Infinite Dimensional Lie Superalgebras, Walter de Gruyter, Berlin, 1992.
  • [4] R. Carles and Y. Diakité, Sur les variétés d'algèbres de Lie de dimension ≤ 7, J. Algebra 91 (1984), 53-63.
  • [5] P. Cartier, Effacement Dans la Cohomologie des Algèbres de Lie, Séminaire Bourbaki 116 (1955), 1-7.
  • [6] L. Corwin, Y. Ne'eman and S. Sternberg, Graded Lie algebras in mathematics and physics (Bose-Fermi symmetry ), Rev. Modern Phys. 47, 3 (1975), 573-603.
  • [7] H. S. Green and P. D. Jarvis, Casimir invariants, characteristic identities and Young diagrams for Colour algebras and superalgebras, J. Math. Phys. 24, 7 (1983), 1681-1687.
  • [8] M. F. Gorodnii, G. B. Podkolzin, Irreducible representations of a graded Lie algebra, in 'Spectral theory of operators and infinite-dimensional analysis', Institute of Mathematics, Academy of Sciences of Ukraine, Kiev, (1984), 66-77.
  • [9] V. G. Kac, Lie Superalgebras, Adv. Math. 26 (1977), 8-96.
  • [10] V. G. Kac, Classification of simple Lie superalgebras, Funct. Anal. Appl. 9 (1975), 263-265.
  • [11] M. V. Karasev, V. P. Maslov, Non-Linear Poisson Brackets. Geometry and Quantization, Trans. Math. Monographs 119, AMS, Providence, 1993.
  • [12] A. A. Kirillov, Yu. A. Neretin, The variety $A_n$ of n-dimensional Lie algebra structures, Am. Math. Soc. Transl. 137 (1987), 21-30.
  • [13] R. Kleeman, Commutation factors on generalized Lie algebras, J. Math. Phys. 26, 10 (1985), 2405-2412.
  • [14] A. K. Kwasniewski, Clifford- and Grassmann- like algebras - Old and new, J. Math. Phys. 26 (1985), 2234-2238.
  • [15] A. K. Kwasniewski, On Graded Lie-like Algebras, Bulletin de la Société des sciences et des lettres de Łódź 39, 6 (1989).
  • [16] J. Lukierski, V. Rittenberg, Color-de Sitter and color-conformal superalgebras, Phys. Rev. D 18, 2 (1978), 385-389.
  • [17] G. M. Mubaragzjanov, Classification of the real structures for Lie algebras of fifth order, Izv. Vyssh. Uchebn. Zaved. Mat. 34, 3 (1963), 99-106, (Russian).
  • [18] W. Marcinek, Colour extensions of Lie algebras and superalgebras, Preprint 746, University of Wrocław (1990).
  • [19] W. Marcinek, Generalized Lie algebras and related topics, Acta Univ. Wratislaviensis (Matematyka, Fizyka, Astronomia) 1170 (1991) I, 3-21, II, 23-52.
  • [20] M. V. Mosolova, Functions of non-commuting operators that generate a graded Lie algebra, Mat. Zametki 29 (1981), 34-45.
  • [21] Yu. A. Neretin, An estimate for the number of parameters defining an n-dimensional algebra, Izv. Acad. Nauk. SSSR 51, 2 (1987), 306-318.
  • [22] V. L. Ostrovskii, S. D. Silvestrov, Representations of the real forms of the graded analogue of a Lie algebra, Ukrain. Mat. Zh. 44, 11 (1992), 1518-1524; (English translation: Ukrainian Math. J. 44, 11 (1993), 1395-1401).
  • [23] A. Pais, V. Rittenberg, Semisimple graded Lie algebras, J. Math. Phys. 16 (1975), 2062-2073.
  • [24] V. Rittenberg, D. Wyler, Generalized Superalgebras, Nucl. Phys. B 139 (1978), 189-202.
  • [25] L. E. Ross, Representations of Graded Lie algebras, Trans. Amer. Math. Soc. 120 (1965), 17-23.
  • [26] Yu. S. Samoilenko, Spectral Theory of Families of Self-adjoint Operators, Kluwer, Dordrecht, 1990.
  • [27] M. Scheunert, The Theory of Lie Superalgebras, Lecture Notes in Mathematics 716 (1979), Springer-Verlag.
  • [28] M. Scheunert, Generalized Lie algebras, J. Math. Phys. 20, 4 (1979), 712-720.
  • [29] M. Scheunert, Graded tensor calculus, J. Math. Phys. 24, 11 (1983), 2658-2670.
  • [30] M. Scheunert, Casimir elements of ε-Lie algebras, J. Math. Phys. 24, 11 (1983), 2671-2680.
  • [31] S. D. Silvestrov, Hilbert space representations of the graded analogue of the Lie algebra of the group of plane motions, Studia Mathematica 117, 2 (1996), 195-203. (Research report 12, Department of Mathematics, Umeå University, (1994)).
  • [32] E. B. Vinberg, V. V. Gorbacevich, A. L. Onischik, Structure of Lie groups and algebras, Itogi Nauki i Tekhniki, Sovremennye problemy matematiki, Fundamentalnye napravleniya, VINITI, Moscow 41 (1990), 1-260.
  • [33] S. Yamaguchi, On some classes of nilpotent Lie algebras and their automorphism groups, Mem. Fac. Sci. Kyushu Univ. A 35, 2 (1981), 341-351.

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Bibliografia

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bwmeta1.element.bwnjournal-article-bcpv40z1p159bwm
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