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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.10162 |
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| _version_ | 1866908954936737792 |
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| author | Subag, Eyal |
| author_facet | Subag, Eyal |
| contents | We introduce a duality for Inönü-Wigner contractions attached to real symmetric Lie algebras. Starting from a symmetric pair $(\mathfrak{g},θ)$, 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 $\mathfrak{g}^θ$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10162 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dual contractions and algebraic families Subag, Eyal Mathematical Physics Rings and Algebras Representation Theory 22E70 We introduce a duality for Inönü-Wigner contractions attached to real symmetric Lie algebras. Starting from a symmetric pair $(\mathfrak{g},θ)$, 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 $\mathfrak{g}^θ$. 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. |
| title | Dual contractions and algebraic families |
| topic | Mathematical Physics Rings and Algebras Representation Theory 22E70 |
| url | https://arxiv.org/abs/2604.10162 |