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arXiv · 2404.17881

Symmetric bilinear forms, superalgebras and integer matrix factorization

Dan Fretwell·Jenny Roberts
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Abstract

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

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Dan Fretwell, Jenny Roberts. 2024-04-27. Symmetric bilinear forms, superalgebras and integer matrix factorization. https://arxiv.org/abs/2404.17881

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