Mathematicians find unexpected bridge between abstract algebra and quantum geometry
Researchers have discovered a novel geometric framework that simplifies how scientists understand complex algebraic structures called semifields—with potential applications in cryptography and quantum computing. The breakthrough emerged from studying how tensors behave over finite fields, revealing unexpected connections to quantum-like geometric surfaces that could reshape how engineers design secure systems.
Originaltitel: The cyclic model for threefold tensors over a finite field: semifields and quasi-Hermitian surfaces
<p>In this paper we study finite dimensional algebras, in particular finite semifields, through their correspondence with nonsingular threefold tensors. We study a particular embedding of the tensor product space into a projective space. This cyclic model allows us to understand tensors and their contractions in a new geometric way, relating the contraction of a tensor to a natural subspace of a subgeometry. This leads us to new results on invariants and classifications of tensors and algebras and on nonsingular fourfold tensors. A detailed study of the geometry of this setup for the case of the threefold tensor power of a vector space of dimension two over a finite field surprisingly leads to a new construction of quasi-Hermitian varieties in PG(3,q2).</p>