对称双线性形式、超代数和整数矩阵因式分解

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2024-07-25 DOI:10.1016/j.laa.2024.07.017

Dan Fretwell, Jenny Roberts

引用次数: 0

摘要

我们构建并研究 EndK(V) 上的某些（非平衡）超代数结构，其中 K 是特征为 0 的域，V 是有限维的 K 向量空间（维数 n≥2）。这些结构由 V 上的非退化对称双线性形式 B 和非零基向量 w∈V 的选择所诱导。在进一步探索了这个结构之后，我们将我们的结果应用于有关整数矩阵因式分解和积分网格等势的某些问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Symmetric bilinear forms, superalgebras and integer matrix factorization

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 $n \geq 2$ ). 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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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.