Event Details

Speaker: Jenny Roberts (Bristol) Title: Symmetric bilinear forms, superalgebras and integer matrix factorization

Abstract: Superalgebras have been of wide importance in mathematics and physics since they provide robust mathematical models of supersymmetry. Today, I will discuss a superalgebra construction with a pure mathematical application. In particular, for a field k and k-vector space V, one can construct a superalgebra decomposition of Endₖ(V) which depends on a symmetric bilinear form on V. I will explain this construction and explore the applications of this to integer matrix factorisation, for some cases allowing us to answer the question: Can a symmetric matrix B be factorised as B=MᵀM for an integer matrix M?