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The Casimir Element


We consider the problem of constructing the Casimir operator of the fourth order for the orthogonal group of the fifth order. The problem is completely solved. The explicit form of the Casimir operator is obtained.

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Corresponding author

Correspondence to N. I. Vishnevskaya.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 3, pp. 43–52, 2013.

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Vishnevskaya, N.I. The Casimir Element. J Math Sci 206, 486–493 (2015).

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  • Invariant Operator
  • Homogeneous Polynomial
  • Orthogonal Group
  • Cartan Subalgebra
  • Casimir Operator