Quasi-algebras were introduced as algebras in a monoidal category. Since the associativity constraints in these categories are allowed to be nontrivial, the class of quasi-algebras contains various important examples of non-associative algebras like the octonions and other Cayley algebras. The diamond lemma is a reduction method used in algebra. The original diamond lemma was stated in graph theory by Newman which was later generalized to associative algebras by Bergman. In this talk, we will see the analog of this lemma for the group graded quasi-algebras with some interesting examples like octonion algebra and generalized octonions

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Last updated: 17 Jan 2019