We study division algebras in an arbitrary linear Gr-category, i.e., a category of finite-dimensional vector spaces graded by a group with associativity constraint given by a 3-cocycle. When the 3-cocycle is non-coboundary, this provides some interesting classes of nonassociative division algebras. In particular, when we work on Gr-categories over the field of real numbers, some quasi-associative version of the quaternions and octonions appear.
"Division algebras in linear Gr-categories." Bull. Belg. Math. Soc. Simon Stevin 21 (5) 859 - 872, december 2014. https://doi.org/10.36045/bbms/1420071858