$\textrm{U}(n)$-structures and their induced minimal left ideals
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918193512054784 |
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| author | Suárez, Ricardo |
| author_facet | Suárez, Ricardo |
| contents | In previous work, we associated to $\textrm{SU(3)}$, $\mathrm{G}_2$, and $\textrm{Spin(7)}$-structures minimal left ideals for the Clifford algebras $\mathbb{R}_{0,6},\mathbb{R}_{0,7}$, and $\mathbb{R}_{0,8}$, respectively. In this paper, we continue to analyze the link between Berger's classification theorem and the structure theorem of minimal left ideals for Clifford algebras of signature $(p,q)$ by identifying $\mathrm{U}(n)$-structures with minimal left ideals for Clifford algebras of various signatures via the induced Kahler polynomial $P(ω_{0})$ associated with the symplectic form $ω_{0}$ that defines the $\mathrm{U}(n)$-structure as a stabilizer subgroup of $\mathrm{O}(n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06900 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\textrm{U}(n)$-structures and their induced minimal left ideals Suárez, Ricardo Differential Geometry In previous work, we associated to $\textrm{SU(3)}$, $\mathrm{G}_2$, and $\textrm{Spin(7)}$-structures minimal left ideals for the Clifford algebras $\mathbb{R}_{0,6},\mathbb{R}_{0,7}$, and $\mathbb{R}_{0,8}$, respectively. In this paper, we continue to analyze the link between Berger's classification theorem and the structure theorem of minimal left ideals for Clifford algebras of signature $(p,q)$ by identifying $\mathrm{U}(n)$-structures with minimal left ideals for Clifford algebras of various signatures via the induced Kahler polynomial $P(ω_{0})$ associated with the symplectic form $ω_{0}$ that defines the $\mathrm{U}(n)$-structure as a stabilizer subgroup of $\mathrm{O}(n)$. |
| title | $\textrm{U}(n)$-structures and their induced minimal left ideals |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2511.06900 |