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arXiv · 2405.18656

Applications of the quaternionic Jordan form to hypercomplex geometry

Adrián Andrada·María Laura Barberis
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Abstract

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 $n$.

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Adrián Andrada, María Laura Barberis. 2024-05-28. Applications of the quaternionic Jordan form to hypercomplex geometry. https://doi.org/10.1016/j.jalgebra.2024.10.023

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