Open Access
2011 Algebraic Structures Derived from Foams
J. Scott Carter, Masahico Saito
J. Gen. Lie Theory Appl. 5: 1-9 (2011). DOI: 10.4303/jglta/G100202


Foams are surfaces with branch lines at which three sheets merge. They have been used in the categorification of $\mathrm{sl}(3)$ quantum knot invariants and also in physics. The $2D$-TQFT of surfaces, on the other hand, is classified by means of commutative Frobenius algebras, where saddle points correspond to multiplication and comultiplication. In this paper, we explore algebraic operations that branch lines derive under TQFT. In particular, we investigate Lie bracket and bialgebra structures. Relations to the original Frobenius algebra structures are discussed both algebraically and diagrammatically.


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J. Scott Carter. Masahico Saito. "Algebraic Structures Derived from Foams." J. Gen. Lie Theory Appl. 5 1 - 9, 2011.


Published: 2011
First available in Project Euclid: 29 September 2011

zbMATH: 1210.57003
MathSciNet: MR2795576
Digital Object Identifier: 10.4303/jglta/G100202

Primary: 16T10 , 17B37 , 57M25 , 81R50

Rights: Copyright © 2011 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

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