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

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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.

Item Type:
Journal Article
Journal or Publication Title:
Linear Algebra and its Applications
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2607
Subjects:
?? discrete mathematics and combinatoricsalgebra and number theorygeometry and topologynumerical analysis ??
ID Code:
222775
Deposited By:
Deposited On:
06 Aug 2024 10:50
Refereed?:
Yes
Published?:
Published
Last Modified:
01 Nov 2024 04:00