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- W4386044105 abstract "The aim of this work is to construct families of weighing matrices via their automorphism group action. This action is determined from the $0,1,2$-cohomology groups of the underlying abstract group. As a consequence, some old and new families of weighing matrices are constructed. These include the Paley Conference, the Projective-Space, the Grassmannian, and the Flag-Variety weighing matrices. We develop a general theory relying on low dimensional group-cohomology for constructing automorphism group actions, and in turn obtain structured matrices that we call emph{Cohomology-Developed matrices}. This Cohomology-Development generalizes the Cocyclic and Group Developments. The Algebraic structure of modules of Cohomology-Developed matrices is discussed, and an orthogonality result is deduced. We also use this algebraic structure to define the notion of emph{quasiproducts}, which is a generalization of the Kronecker-product." @default.
- W4386044105 created "2023-08-22" @default.
- W4386044105 creator A5009115329 @default.
- W4386044105 date "2019-03-01" @default.
- W4386044105 modified "2023-09-25" @default.
- W4386044105 title "Cohomology-Developed Matrices -- constructing families of weighing matrices and automorphism actions" @default.
- W4386044105 doi "https://doi.org/10.48550/arxiv.1903.00471" @default.
- W4386044105 hasPublicationYear "2019" @default.
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