The Hurwitz determinants and the signatures of irreducible representations of simple real Lie algebras

• Autorzy: Alexander Rudy
• Języki publikacji: EN

Abstrakty

EN

The paper deals with the real classical Lie algebras and their finite dimensional irreducible representations. Signature formulae for Hermitian forms invariant relative to these representations are considered. It is possible to associate with the irreducible representation a Hurwitz matrix of special kind. So the calculation of the signatures is reduced to the calculation of Hurwitz determinants. Hence it is possible to use the Routh algorithm for the calculation.

Słowa kluczowe

EN

Lie algebras; signature formulae; Hurwitz matrix; Routh algorithm; 17B10; 17B20

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2005
• Tom: 3
• Numer: 4
• Strony: 606-613

Daty

wydano

2005-12-01

online

2005-12-01

Twórcy

autor

Alexander Rudy

• Belarus National Technical University

Bibliografia

• [1] F.I. Karpelevich: “Simple subalgebras of real Lie algebras”, Trudy Mosk. Mat. Obshch., Vol. 4, (1955), pp. 3–112.
• [2] J. Patera and R.T. Sharp: “Signatures of finite su representations”, J. Math. Phys., Vol. 25, (1984), pp. 2128–2131, MR0748387 (85j:22042). http://dx.doi.org/10.1063/1.526420
• [3] A.N. Rudy: “Signatures of finite representation of real, simple Lie algebras”, J. Phys. A: Math. Gen., Vol. 26, (1993), pp. 5873–5880, MR1252794(94i:17014). http://dx.doi.org/10.1088/0305-4470/26/21/025
• [4] A.N. Rudy: “Signatures of finite classical Lie algebra representations”, J. Phys. A:Math. Gen., Vol. 28 (1995), pp. 1641–1653, MR1338050(96e:17017). http://dx.doi.org/10.1088/0305-4470/28/6/018
• [5] N. Burbaki: Groupes et algebras de Lie. Ch. IV–VI, Hermann, Paris, 1968.
• [6] F.R. Gantmacher: The theory of matrices, AMS Chelsea Publishing, Providence, RI, 1959.

Identyfikatory

DOI

10.2478/BF02475621