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

Studia Mathematica (1996)

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

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topSilvestrov, 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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- [5] W. Marcinek, Generalized Lie algebras and related topics, 1, 2, Acta Univ. Wratislav. Mat. Fiz. Astronom. 55 (1991). Zbl0762.17022
- [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. Zbl0423.17004
- [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. Zbl0423.17003
- [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.

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