Symmetric bilinear forms, superalgebras and integer matrix factorization

Fretwell, Dan and Roberts, Jenny (2024) Symmetric bilinear forms, superalgebras and integer matrix factorization. Linear Algebra and its Applications, 700. pp. 61-79. ISSN 0024-3795

Abstract

We construct and investigate certain (unbalanced) superalgebra structures on End_ (V), with K a field of characteristic 0 and V a finite dimensional K-vector space (of dimension n ≥ 2). These structures are induced by a choice of non-degenerate symmetric bilinear form B on V and a choice of non-zero base vector w ∈ V. After exploring the construction further, we apply our results to certain questions concerning integer matrix factorization and isometry of integral lattices.