The super counterparts of both unital composition algebras and of symmetric composition algebras are classified. It turns out that new objects arise only over fields of characteristic 3. The Principle of Local Triality is considered for this new objects. It is related to some order 3 automorphisms of the simple Lie superalgebras osp(1, 2) and osp(4,2) in characteristic 3. [References: 16]
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