ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

7. Lie Groups and Lie Algebras

1991 MS Classification: 15, 16, 22, 35 Barannyk, Lyudmyla L., Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine Barannyk, Leonid F., Pedagogical University, Słupsk, Poland On an algorithm for classifying subalgebras of the Poincaré algebra AP (2, n) The Poincaré algebra AP (2, n) contains as subalgebras the pseudoorthogonal algebra AO(2, n) that is isomorphic with the conformal algebra AC(1, n − 1), the Poincaré algebra AP (1, n), the extended Poincaré algebra AP̃(1, n − 1), the extended Galilean algebra AG_{2}(1, n − 1), the full Galilean algebra AG_{4}(n − 2). Subalgebras of each of these algebras were used to construct invariant solutions to many nonlinear equations of mathematical physics. The procedure of constructing invariant solutions stipulates that subalgebras of an invariance algebra for a given equation are beforehand classified up to the conjugation with respect to the group of inner automorphisms of this algebra. We substantiate an algorithm for classifying subalgebras of the algebra AP (2, n) for an arbitrary n ≥ 3 up to the conjugation with respect to the group of inner automorphisms of this algebra. Reference: L. L. Barannyk, and L. F. Barannyk, On classification of subalgebras of the Poincaré algebra AP (2, n), Dopovidi Nats. Akad. Nauk Ukrainy 8 (1998) (in Ukrainian, to appear).