Matrix factorizations and double line in ${\mathfrak{sl}}_n$ quantum link invariant

Abstract

This article gives matrix factorizations for the trivalent diagrams and double line appearing in ${\mathfrak{sl}}_n$ quantum link invariant. These matrix factorizations reconstruct Khovanov-Rozansky homology. And we show that the Euler characteristic of the matrix factorization for a double loop equals the quantum dimension of the representation ${\wedge }^{2}V$ of $U_q({\mathfrak{sl}}_n)$ in Section \ref{sec3.3}.

17 pages

References in corpus (7)

• Khovanov's homology for tangles and cobordisms
• Spiders for rank 2 Lie algebras
• Note on Khovanov link cohomology
• Some differentials on Khovanov-Rozansky homology
• Matrix Factorizations and Kauffman Homology
• Virtual crossings, convolutions and a categorification of the SO(2N) Kauffman polynomial
• Khovanov-Rozansky homology via a canopolis formalism

Cited by in corpus (1)

• Matrix factorizations and colored MOY graphs