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Supersymmetries and Quantum Symmetries pp 322–329Cite as

Characteristic polynomials for quantum matrices

  • Quantum Field Theory And Quantum Groups
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Part of the book series: Lecture Notes in Physics ((LNP,volume 524))

Abstract

A quantum version of the Cayley-Hamilton theorem is found for the matrix T of the generators of the RTT-algebra. In the quasitriangular case, a connection between the characteristic identities in the RTT and RE-algebras is established.

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References

  • Reshetikhin N., Takhtadjan L. and Faddeev L., Quantization of Lie groups and Lie algebras, Algebra i Analiz, 1 No. 1 (1989) 178–206. English translation in: Leningrad Math. J. 1 (1990) 193–225.

    Google Scholar 

  • Nazarov M. and Tarasov V., Yangians and Gelfand-Zetlin bases, Publications RIMS 30 (1994) 459–478.

    Article  MATH  MathSciNet  Google Scholar 

  • Pyatov P.N. and Saponov P.A., Characteristic Relations for Quantum Matrices, J. Phys. A: Math. Gen., 28 (1995) 4415–4421.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • Gurevich D.I., Pyatov P.N. and Saponov P.A., Hecke Symmetries and Characteristic Relations on Reflection Equation Algebras, Preprint JINR E-95-202, q-alg/9606.

    Google Scholar 

  • Ewen H., Ogievetsky O. and Wess J., Quantum matrices in two dimensions, Lett. Math. Phys., 22 (1991) 297–305.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Gurevich D.I., Algebraic aspects of the quantum Yang-Baxter equation, Algebra i Analiz, 2 (1990) 119–148. English translation in: Leningrad Math. J. 2 (1991) 801–828.

    MATH  MathSciNet  Google Scholar 

  • Maillet J.M., Lax equations and quantum groups, Phys. Lett. B245 (1990) 480–486.

    ADS  MathSciNet  Google Scholar 

  • Pyatov P.N. and Saponov P.A., Newton relations for quantum matrix algebras of RTT-type, Preprint IHEP 96-76.

    Google Scholar 

  • Reshetikhin N., Quasitriangular Hopf algebras and invariants of tangles, Algebra i Analiz, 1 No. 2 (1989) 169–188. English translation in: Leningrad Math. J. 1 (1990) 491–513.

    MathSciNet  Google Scholar 

  • Reshetikhin N.Yu. and Semenov-Tian-Shansky M.A., Quantum R-matrices and factorization problem, Geometry and Physics 5 No.4 (1988) 533–550.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • Drinfeld V.G., On almost cocommutative Hopf algebras, Algebra i Analiz, 1 No. 2 (1989) 30–46. English translation in: Leningrad Math. J. 1 (1990) 321–342.

    MathSciNet  Google Scholar 

  • Schupp P., Watts P. and Zumino B., Bicovariant quantum algebras and quantum Lie algebras, Comm.Math.Phys. 157 (1993) 305–329.

    Article  MATH  ADS  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Bogoliubov Laboratory of Theoretical Physics, JINR, 141980, Dubna Moscow Reg., Russia

    A. Isaev & P. Pyatov

  2. Center of Theoretical Physics, Luminy, 13288, Marseille, France

    O. Ogievetsky

  3. Theoretical Department, P. N. Lebedev Physical Institute, Leninsky pr. 53, 117924, Moscow, Russia

    O. Ogievetsky

  4. Theory Department, IHEP, 142284, Protvino, Moscow region, Russia

    P. Saponov

Authors
  1. A. Isaev
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  2. O. Ogievetsky
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  3. P. Pyatov
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  4. P. Saponov
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Editor information

Julius Wess Evgeny A. Ivanov

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© 1999 Springer-Verlag

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Isaev, A., Ogievetsky, O., Pyatov, P., Saponov, P. (1999). Characteristic polynomials for quantum matrices. In: Wess, J., Ivanov, E.A. (eds) Supersymmetries and Quantum Symmetries. Lecture Notes in Physics, vol 524. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0104613

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  • DOI: https://doi.org/10.1007/BFb0104613

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66004-0

  • Online ISBN: 978-3-540-48795-1

  • eBook Packages: Springer Book Archive

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