Hilbert space representations of the graded analogue of the Lie algebra of the group of plane motions

• Autorzy: Sergei D. Silvestrov
• Języki publikacji: EN

Abstrakty

EN

The irreducible Hilbert space representations of a ⁎-algebra, the graded analogue of the Lie algebra of the group of plane motions, are classified up to unitary equivalence.

Kategorie tematyczne

• 47L60: Algebras of unbounded operators; partial algebras of operators
• 17A45: Quadratic algebras (but not quadratic Jordan algebras)
• 16W55: ``Super'' (or ``skew'') structure

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1995-1996
• Tom: 117
• Numer: 2
• Strony: 195-203

Daty

wydano

1996

otrzymano

1995-05-25

poprawiono

1995-08-16

Twórcy

autor

Sergei D. Silvestrov

• Department of Mathematics, University Of Umeå, S-90187 Umeå, Sweden

Bibliografia

• [1] M. F. Barnsley, Fractals Everywhere, Academic Press, New York, 1988.
• [2] 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.
• [3] M. V. Karasev and V. P. Maslov, Non-Lie permutation relations, Russian Math. Surveys 45 (5) (1990), 51-98.
• [4] A. K. Kwaśniewski, Clifford- and Grassmann-like algebras - old and new, J. Math. Phys. 26 (1985), 2234-2238.
• [5] W. Marcinek, Generalized Lie algebras and related topics, 1, 2, Acta Univ. Wratislav. Mat. Fiz. Astronom. 55 (1991).
• [6] V. L. Ostrovskiĭ and Yu. S. Samoĭlenko, Unbounded operators satisfying non-Lie commutation relations, Rep. Math. Phys. 28 (3) (1989), 93-106.
• [7] V. L. Ostrovskiĭ and S. D. Silvestrov, Representations of the real forms of the graded analogue of a Lie algebra, Ukrain. Mat. Zh. 44 (11) (1992), 1518-1524 (in Russian).
• [8] V. Rittenberg and D. Wyler, Generalized superalgebras, Nuclear Phys. B 139 (1978), 189-202.
• [9] Yu. S. Samoĭlenko, Spectral Theory of Families of Self-Adjoint Operators, Kluwer, Dordrecht, 1990.
• [10] M. Scheunert, Generalized Lie algebras, J. Math. Phys. 20 (1979), 712-720.
• [11] S. D. Silvestrov, On the classification of 3-dimensional graded ε-Lie algebras, Research Reports Series, No. 2, Department of Mathematics, Umeå University, 1993, 49 pp.
• [12] S. D. Silvestrov, The classification of 3-dimensional graded ε-Lie algebras, to appear.