Call an element of a finite field positive when it is a nonzero square, and call a matrix over that field totally positive when every one of its minors is positive. Ayyer and Prasad, who introduced this class, ask for the least prime power q admitting an m…
Matsuo algebras are the commutative non-associative algebras attached to groups of 3-transpositions; they are the axial algebras of Jordan type that come from a group, and for η ≠ 1/2 every algebra of Jordan type η is one of them or a quotient of one. A rec…
A Krasner hyperfield is a field-like structure whose addition is multivalued. Let Hₙ denote the number of isomorphism classes of hyperfields of order n. The values H₂, …, H₆ = 2, 5, 7, 27, 16 are due to Ameri, Eyvazi and Hošková-Mayerová and H₇ = 277 to Mas…
For a simple Lie algebra L over a finite field, Kishnani and Singh define k(L) to be the least k such that every non-zero a ∈ L occurs as the first entry of some generating k-tuple, and observe that no clear answer for k(L) seems to be known; the number is…
