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Submission: 2005, May 5
Tensor categorical and diagrammatic techniques used in the theory of knot invariants can be applied to compute the dimension and other numerical invariants for certain algebraic structures defined by tensor identities. These techniques are described, and applied to symmetric composition algebras and $3$-vector products.
2000 Mathematics Subject Classification: Primary 17A75; Secondary 81T99
Keywords and Phrases: tensor categories, composition algebras, vector products
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