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This work aims to efficiently generate Lie group invariants for inhomogeneous polynomial vector spaces.

March 29, 2026Journal of Lie theoryOpen Access

Lie Group Invariants of Inhomogeneous Polynomial Vector Spaces

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This work aims to efficiently generate Lie group invariants for inhomogeneous polynomial vector spaces.
Utilized the Cartan method of moving frames for derivation.
Applied results to inhomogeneous cubic polynomials in two variables.
Analyzed the actions of the Euclidean group and the general affine group.
Identified twelve distinct classes of canonical forms for cubic polynomials.
Developed a compact indicial notation for expressing the invariants.
Created a global system of invariants separating associated orbits.

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Method generates Lie group invariants for polynomial vector spaces, suggesting effective classification strategies.

J. T. Horwood (2007) studied this question.

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