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arXiv · 2604.10162

Dual contractions and algebraic families

Eyal Subag
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Abstract

We introduce a duality for In\"{o}n\"{u}-Wigner contractions attached to real symmetric Lie algebras. Starting from a symmetric pair $(\mathfrak{g},\theta)$, we define a dual real form $\mathfrak{g}^{*}$ inside the complexification of $\mathfrak{g}$ and consider the corresponding contraction with respect to the common fixed-point subalgebra $\mathfrak{g}^{\theta}$. The main result shows that the original contraction and its dual appear as real fibers of a single algebraic family of complex Lie algebras equipped with an anti-holomorphic involution. This places the two contractions in one geometric framework and connects them with the algebraic-family methods developed in recent work on contractions, real forms, and hidden symmetries.

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Eyal Subag. 2026-04-11. Dual contractions and algebraic families. https://arxiv.org/abs/2604.10162

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