${\mathbb{Z}}_2^n$-graded quasialgebras and the Hurwitz problem on compositions of quadratic forms

Ya-Qing Hu, Hua-Lin Huang, Chi Zhang

We introduce a series of ${\mathbb{Z}}_2^n$-graded quasialgebras $\bbP_n(m)$ which generalizes Clifford algebras, higher octonions, and higher Cayley algebras. The constructed series of alge…