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The aim is to establish an invariant theory for inductive limits of infinite-dimensional groups acting on modules and related structures.

March 29, 2026Journal of Lie theoryOpen Access

Invariant Theory of a Class of Infinite-Dimensional Groups

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The aim is to establish an invariant theory for inductive limits of infinite-dimensional groups acting on modules and related structures.
Developed a coherent invariant theory framework for infinite-dimensional groups.
Proved the Fundamental Theorem of Invariant Theory in the context of these groups.
Introduced a notion of basis for the rings of invariants and generalized Hilbert's Finiteness Theorem.
Discussed key concepts from classical invariant theory, such as Hilbert's Nullstellensatz.
Established a comprehensive invariant theory for inductive limits of groups.
Provided examples of invariants related to infinite-dimensional classical groups.
Generalized important notions like the primeness of ideals of invariants, enhancing classical theories.

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This article develops invariant theory for infinite-dimensional groups acting on modules, suggesting new insights into classical concepts.

Ton-That et al. (2003) studied this question.

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This article develops invariant theory for infinite-dimensional groups acting on modules, suggesting new insights into classical concepts.