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THE QUANTUM 𝔰𝔩(3) INVARIANTS OF CUBIC BIPARTITE PLANAR GRAPHS

DONGSEOK KIM

Department of Mathematics, Kyonggi University, Suwon, 443-760, Korea

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and

JAEUN LEE

Department of Mathematics, Yeungnam University, Kyongsan, 712-749, Korea

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https://doi.org/10.1142/S0218216508006142Cited by:2 (Source: Crossref)

Abstract

Temperley–Lieb algebras have been generalized to 𝔰𝔩(3,ℂ) web spaces. Since a cubic bipartite planar graph with suitable directions on edges is a web, the quantum 𝔰𝔩(3) invariants naturally extend to all cubic bipartite planar graphs. First we completely classify them as a connected sum of prime webs. We provide a method to find all prime webs. Using the quantum 𝔰𝔩(3) invariants, we provide a criterion which determines the symmetry of cubic bipartite planar graphs. We also provide an example that our criterions for graphs is different from that of links.

Keywords:

AMSC: 57M27, 57M15

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