Lie algebra admitted by the differential system s³(3) and functional basis of invariants polynomials

Abstract

The Lie algebra of the representation of the centro-affine group in the space of coefficients, phase variables and covariant vector coordinates for the ternary differential system with third-degree homogeneities s³(3) was obtained. Using this algebra, the number of elements in the functional basis of invariant centro-affine polynomials (invariants, comitants, contravariants, mixed comitants) was determined and irreductible elements from these bases were obtained, and for the comitants and contravariants a functional basis was constructed.