nLab
Moore-Seiberg data

Moore–Seiberg data are structure constants for a modular tensor category, seen as a Frobenius algebra in the 2-category of Vect kVect_k-enriched abelian categories. More explicitely, Moore–Seiberg data for the modular tensor category 𝒞\mathcal{C} are the collections of kk-vector spaces

X 1,,X n=Hom 𝒞(1,X 1X n), \langle X_1,\dots,X_n\rangle=Hom_\mathcal{C}(\mathbf{1},X_1\otimes\cdots\otimes X_n),

where 1\mathbf{1} is the unit object of 𝒞\mathcal{C}.

References

Bojko Bakalov and Alexander Kirillov, Lectures on Tensor Categories and Modular Functors, University Lecture Series 21, AMS.

Gregory Moore and Nathan Seiberg, Classical and quantum conformal field theory, Comm. Math. Phys. 123 (1989), 177–254.

Revised on June 8, 2010 17:22:18 by Toby Bartels (75.88.75.61)