On the automorphism of Barns Wall Lattice Λ_BW₁₆ and rank 4 tensor of quaternions

2022/10/08 by Misaki Ohta, Ohta, Misaki
Mathematics · #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2210.05609

Abstract

In a previous paper, I found that the Weyl group W(F₄) and Barns-Wall Lattice BW₁₆ can be constructed using the rank 2 tensor of the quaternion. In the present paper, I describe how I were able to construct an algebra, which is the subalgebra of the direct product of Hurwitz Quaternionic integers \mathscrH⁴, isomorphic to the automorphism Aut(BW₁₆) order 2²¹ ⋅ 3⁵ ⋅ 5² ⋅ 7 of Barns Wall Lattice BW₁₆ by functionally extending the rank of the tensor product of quaternions to 4.

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