Applications of the quaternionic Jordan form to hypercomplex geometry
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912099151642624 |
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| author | Andrada, Adrián Barberis, María Laura |
| author_facet | Andrada, Adrián Barberis, María Laura |
| contents | We apply the quaternionic Jordan form to classify the hypercomplex nilpotent almost abelian Lie algebras in all dimensions and to carry out the complete classification of 12-dimensional hypercomplex almost abelian Lie algebras. Moreover, we determine which 12-dimensional simply connected hypercomplex almost abelian Lie groups admit lattices. Finally, for each integer $n>1$ we construct infinitely many, up to diffeomorphism, $(4n+4)$-dimensional hypercomplex almost abelian solvmanifolds which are completely solvable. These solvmanifolds arise from a distinguished family of monic integer polynomials of degree $n$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_18656 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Applications of the quaternionic Jordan form to hypercomplex geometry Andrada, Adrián Barberis, María Laura Differential Geometry 53C26, 22E25, 22E40, 53C55 We apply the quaternionic Jordan form to classify the hypercomplex nilpotent almost abelian Lie algebras in all dimensions and to carry out the complete classification of 12-dimensional hypercomplex almost abelian Lie algebras. Moreover, we determine which 12-dimensional simply connected hypercomplex almost abelian Lie groups admit lattices. Finally, for each integer $n>1$ we construct infinitely many, up to diffeomorphism, $(4n+4)$-dimensional hypercomplex almost abelian solvmanifolds which are completely solvable. These solvmanifolds arise from a distinguished family of monic integer polynomials of degree $n$. |
| title | Applications of the quaternionic Jordan form to hypercomplex geometry |
| topic | Differential Geometry 53C26, 22E25, 22E40, 53C55 |
| url | https://arxiv.org/abs/2405.18656 |