Abstract
This is the third part in a series of papers developing a twisted tensor product theory for nonlocal vertex algebras and its modules. In this paper we introduce and study twisted tensor product modules over Möbius twisted tensor product nonlocal vertex algebras. Among the main results, we find the isomorphic relation between the opposite Möbius twisted tensor product nonlocal vertex algebra and twisted tensor product of opposite Möbius nonlocal vertex algebras. And we also establish the isomorphism between two twisted tensor product contragredient modules. Furthermore, we study iterated twisted tensor product modules over iterated twisted tensor product nonlocal vertex algebras and find conditions for constructing an iterated twisted tensor product module of three factors.
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