ArticleOriginal scientific text

Title

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

Authors 1

Affiliations

  1. Department of Mathematics, University Of Umeå, S-90187 Umeå, Sweden

Abstract

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.

Bibliography

  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.
Pages:
195-203
Main language of publication
English
Received
1995-05-25
Accepted
1995-08-16
Published
1996
Exact and natural sciences