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

Sergei Silvestrov

Studia Mathematica (1996)

  • Volume: 117, Issue: 2, page 195-203
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Silvestrov, Sergei. "Hilbert space representations of the graded analogue of the Lie algebra of the group of plane motions." Studia Mathematica 117.2 (1996): 195-203. <http://eudml.org/doc/216251>.

@article{Silvestrov1996,
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.},
author = {Silvestrov, Sergei},
journal = {Studia Mathematica},
keywords = {irreducible Hilbert space representations; -algebra; Lie algebra of the group of plane motions},
language = {eng},
number = {2},
pages = {195-203},
title = {Hilbert space representations of the graded analogue of the Lie algebra of the group of plane motions},
url = {http://eudml.org/doc/216251},
volume = {117},
year = {1996},
}

TY - JOUR
AU - Silvestrov, Sergei
TI - Hilbert space representations of the graded analogue of the Lie algebra of the group of plane motions
JO - Studia Mathematica
PY - 1996
VL - 117
IS - 2
SP - 195
EP - 203
AB - 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.
LA - eng
KW - irreducible Hilbert space representations; -algebra; Lie algebra of the group of plane motions
UR - http://eudml.org/doc/216251
ER -

References

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  1. [1] M. F. Barnsley, Fractals Everywhere, Academic Press, New York, 1988. 
  2. [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. Zbl0557.17004
  3. [3] M. V. Karasev and V. P. Maslov, Non-Lie permutation relations, Russian Math. Surveys 45 (5) (1990), 51-98. Zbl0727.16025
  4. [4] A. K. Kwaśniewski, Clifford- and Grassmann-like algebras - old and new, J. Math. Phys. 26 (1985), 2234-2238. Zbl0583.15018
  5. [5] W. Marcinek, Generalized Lie algebras and related topics, 1, 2, Acta Univ. Wratislav. Mat. Fiz. Astronom. 55 (1991). Zbl0762.17022
  6. [6] V. L. Ostrovskiĭ and Yu. S. Samoĭlenko, Unbounded operators satisfying non-Lie commutation relations, Rep. Math. Phys. 28 (3) (1989), 93-106. 
  7. [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. [8] V. Rittenberg and D. Wyler, Generalized superalgebras, Nuclear Phys. B 139 (1978), 189-202. Zbl0423.17004
  9. [9] Yu. S. Samoĭlenko, Spectral Theory of Families of Self-Adjoint Operators, Kluwer, Dordrecht, 1990. 
  10. [10] M. Scheunert, Generalized Lie algebras, J. Math. Phys. 20 (1979), 712-720. Zbl0423.17003
  11. [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. [12] S. D. Silvestrov, The classification of 3-dimensional graded ε-Lie algebras, to appear. 

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