2023/11/29 by Lia, Stefano, Sheekey, John
#11E39 #12K10 #14N07 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2311.17896
In this paper we study finite dimensional algebras, in particular finite semifields, through their correspondence with nonsingular threefold tensors. We introduce a alternative embedding of the tensor product space into a projective space. This model allows us to understand tensors and their contractions in a new geometric way, relating the contraction of a tensor with 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).