A remark on the invariant theory of real Lie groups

TL;DR

This paper shows that for certain real Lie groups, their invariant theory aligns with that of their algebraic counterparts, including non-compact orthogonal and symplectic groups, simplifying their study.

Contribution

It provides a straightforward remark establishing the equivalence of invariant theories between specific real Lie groups and their algebraic versions, clarifying their relationship.

Findings

Invariant theory of certain real Lie groups matches that of their algebraic counterparts.

Applicable to non-compact orthogonal and symplectic Lie groups.

Simplifies understanding of invariants in real Lie group contexts.

Abstract

We present a simple remark that assures that the invariant theory of certain real Lie groups coincides with that of the underlying affine, real algebraic groups. In particular, this result applies to the non-compact orthogonal or symplectic Lie groups.