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Original Articles

The number of independent traces and supertraces on symplectic reflection algebras

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Pages 308-335 | Received 15 Aug 2013, Accepted 19 Mar 2014, Published online: 24 Jun 2014

References

  • K.A. Brown, I. Gordon, “Poisson orders, symplectic reflection algebras and representation theory”, J. Reine Angew. Math. 559 (2003), 193–216; arXiv:math/0201042v2 [math.RT].
  • P. Etingof and V. Ginzburg, “Symplectic reflection algebras, Calogero–Moser space, and deformed Harish–Chandra homomorphism”, Inv. Math. 147 (2002), 243–348.
  • I.N. Herstein, “On the Lie and Jordan rings of a simple associative ring”, Amer. J. Math 77 (1955), 279–285.
  • I.N. Herstein, “Topics in Ring Theory”, Chicago Lecture Notes in Math, University of Chicago Press, 1969.
  • S.E. Konstein, “3-particle Calogero Model: Supertraces and Ideals on the Algebra of Observables”, Theor.Math.Phys. 116 (1998) 836–845; arXiv:hep-th/9803213.
  • S.E. Konstein, “An example of simple Lie superalgebra with several invariant bilinear forms”, Resenhas IME-USP 2004; Vol. 6 No. 2/3, 249-255; arXiv:math-ph/0112063.
  • S.E. Konstein and I.V. Tyutin, “Traces on the Superalgebra of Observables of Rational Calogero Model based on the Root System”, Journal of Nonlinear Mathematical Physics, 20:2 (2013), 271–294; arXiv:1211.6600; arXiv:math-ph/9904032.
  • S.E. Konstein and R. Stekolshchik, “Klein operator and the Number of Traces and Supertraces on the Superalgebra of Observables of Rational Calogero Model based on the Root System”, Journal of Nonlinear Mathematical Physics, Vol. 20:2 (2013), 295–308; arXiv:0811.2487; arXiv:1212.0508.
  • S.E. Konstein and M.A. Vasiliev, “Supertraces on the Algebras of Observables of the Rational Calogero Model with Harmonic Potential”, J. Math. Phys. 37 (1996), 2872.
  • I. Losev, “Completions of symplectic reflection algebras”, arXiv:1001.0239v4.
  • S. Montgomery, “Constructing simple Lie superalgebras from associative graded algebras”, J. of Algebra 195 (1997), 558.
  • D.S. Passman, Infinite Crossed Products, Pure and Applied Math vol. 135 Academic Press, San Diego, 1989.
  • M.A. Vasil'ev, “Quantization on sphere and high-spin superalgebras”, JETP Letters, 50 (1989) 344–347; M.A. Vasiliev, “Higher spin algebras and quantization on the sphere and hyperboloid”, Int. J. Mod. Phys. A6 (1991) 1115.

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