Author： Rumynin D.
Publisher： Springer Publishing Company
ISSN： 0037-4466
Source： Siberian Mathematical Journal, Vol.54, Iss.5, 2013-09, pp. : 905-921
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Abstract
We study the algebras that are defined by identities in the symmetric monoidal categories; in particular, the Lie algebras. Some examples of these algebras appear in studying the knot invariants and the Rozansky-Witten invariants. The main result is the proof of the Westbury conjecture for a K3-surface: there exists a homomorphism from a universal simple Vogel algebra into a Lie algebra that describes the Rozansky-Witten invariants of a K3-surface. We construct a language that is necessary for discussing and solving this problem, and we formulate nine new problems.
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