What question did this study set out to answer?

The aim is to explore the Lie algebra related to the centro-affine group and to find invariant polynomials associated with a ternary differential system.

February 17, 2026Open Access

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

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Key Points

The aim is to explore the Lie algebra related to the centro-affine group and to find invariant polynomials associated with a ternary differential system.
Obtained the Lie algebra for the centro-affine group representation.
Determined the number of elements in the functional basis of invariant polynomials.
Constructed functional bases for comitants and contravariants.
Identified the number of invariant centro-affine polynomials.
Obtained irreducible elements from the invariant polynomial bases.
Established a functional basis for comitants and contravariants.

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.

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Lidia Mușinschi (Thu,) studied this question.

synapsesocial.com/papers/699405254e9c9e835dfd5fe8 — DOI: https://doi.org/10.36120/2587-3644.v20i2.62-82

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Moldova State University

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

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Abstract

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Authors

Journals

Actions

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