Hua-Lin Huang (Shandong University)

Algebras in Gr-categories and the Hurwitz Problem on Sum of Squares

Abstract:

We give a brief introduction to braided linear Gr-categories and algebras therein. Some interesting classes of these algebras are applied to the Hurwitz problem on compositions of quadratic forms. In particular, we provide explicit expressions of the well-known Hurwitz-Radon square identities in a uniform way, recover the Yuzvinsky-Lam-Smith formulas, confirm the third family of admissible triples proposed by Yuzvinsky in 1984, improve the two infinite families of solutions obtained recently by Lenzhen, Morier-Genoud and Ovsienko, and construct several new infinite families of solutions.