Symmetric bilinear forms, superalgebras and integer matrix factorization

Fretwell, Dan and Roberts, Jenny (2024) Symmetric bilinear forms, superalgebras and integer matrix factorization. Other. UNSPECIFIED.

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Abstract

We construct and investigate certain (unbalanced) superalgebra structures on End_K(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 in V. After exploring the construction further, we apply our results to certain questions concerning integer matrix factorization and isometry of integral lattices.