Free nilpotent and $H$-type Lie algebras. Combinatorial and orthogonal designs
Differential Geometry
2015-05-19 v3 Representation Theory
Abstract
The aim of our paper is to construct pseudo -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 -type algebras, which implies the existence of lattices on the corresponding pseudo -type Lie groups. Our approach substantially uses combinatorics and reveals the interplay of pseudo -type algebras with combinatorial and orthogonal designs. One of the key tools is the family of Hurwitz-Radon orthogonal matrices.
Keywords
Cite
@article{arxiv.1410.3767,
title = {Free nilpotent and $H$-type Lie algebras. Combinatorial and orthogonal designs},
author = {Kenro Furutani and Irina Markina and Alexander Vasil'ev},
journal= {arXiv preprint arXiv:1410.3767},
year = {2015}
}