Graded Medial n-Ary Algebras and Polyadic Tensor Categories

- Algebras in Tensor Categories

We define and systematically study nonassociative C *-algebras as C *-algebras internal to a topological tensor category. We also offer a concrete approach to these C *-algebras, as G-invariant, norm closed *-subalgebras of bounded operators on a G-Hilbert space, with deformed composition product. Our central results are those of stabilization and Takai duality for (twisted) crossed products in...

algebras , operads and tensor categories

We study the operadic and categorical formulations of (conformal) full field algebras. In particular, we show that a grading-restricted R × R-graded full field algebra is equivalent to an algebra over a partial operad constructed from spheres with punctures and local coordinates. This result is generalized to conformal full field algebras over V L ⊗ V R , where V L and V R are two vertex operat...

On $n$-ary Hypergroups and Fuzzy $n$-ary Homomorphism

On functors between module categories for associative algebras and for N-graded vertex algebras

We prove that the weak associativity for modules for vertex algebras are equivalent to a residue formula for iterates of vertex operators, obtained using the weak associativity and the lower truncation property of vertex operators, together with a known formula expressing products of components of vertex operators as linear combinations of iterates of components of vertex operators. By requirin...

Affine Lie algebras and vertex tensor categories

In this paper, we apply the general theory of tensor products of modules for a vertex operator algebra developed in [HL1]–[HL6] and [H1]–[H2] to the case of the Wess-Zumino-Novikov-Witten models (WZNW models) and related models in conformal field theory. Together with these papers, this paper, among other things, completes the solution of the open problem of constructing the desired braided ten...