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arXiv · 1410.3767

Free nilpotent and $H$-type Lie algebras. Combinatorial and orthogonal designs

Kenro Furutani·Irina Markina·Alexander Vasil'ev
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Abstract

The aim of our paper is to construct pseudo $H$-type algebras from the covering free nilpotent two-step Lie algebra as the quotient algebra by an ideal. We propose an explicit algorithm of construction of such an ideal by making use of a non-degenerate scalar product. Moreover, as a bypass result, we recover the existence of a rational structure on pseudo $H$-type algebras, which implies the existence of lattices on the corresponding pseudo $H$-type Lie groups. Our approach substantially uses combinatorics and reveals the interplay of pseudo $H$-type algebras with combinatorial and orthogonal designs. One of the key tools is the family of Hurwitz-Radon orthogonal matrices.

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Kenro Furutani, Irina Markina, Alexander Vasil'ev. 2014-10-14. Free nilpotent and $H$-type Lie algebras. Combinatorial and orthogonal designs. https://arxiv.org/abs/1410.3767

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