Generalized twistors of nonlocal vertex algebras

Abstract

We introduce and study the concept of (weak) pseudotwistor for a nonlocal vertex algebra, as a generalization of the notion of twistor. We give the relations between pseudotwistors and twisting operators. Furthermore, we study the inverse of an invertible weak pseudotwistor and the composition of two weak pseudotwistors.

Key words： Twistor; pseudotwistor; nonlocal vertex algebra; twisting operator

References

1 BakalovB, KacV G. Field algebras. Int Math Res Not, 2003, 3: 123–159

2 BorcherdsR. Quantum vertex algebras. In: Taniguchi Conference on Mathematics Nara’98. Adv Stud Pure Math, 31. Tokyo: Math Soc Japan, 2001, 51–74

3 CapA, SchichlH, VanzuraJ. On twisted tensor products of algebras. Comm Algebra, 1995, 23: 4701–4735

4 LepowskyJ, LiH. Introduction to Vertex Operator Algebras and Their Representations. Boston: Birkhäuser, 2003

5 LiH. Axiomatic G1-vertex algebras. Commun Contemp Math, 2003, 5: 281–327

6 LiH, SunJ. Twisted tensor products of nonlocal vertex algebras. J Algebra, 2011, 345: 266–294

7 LiH, SunJ. Regular representations of Möbius quantum vertex algebras (in preparation)

8 PanaiteF, OystaeyenF V. Twisted algebras, twisted bialgebras and Rota-Baxter type operators. ArXiv: 1502.05327v2

9 PenaJ, PanaiteF, OystaeyenF V. General twisting of algebras. Adv Math, 2007, 212: 315–337

10 SunJ. Iterated twisted tensor products of nonlocal vertex algebras. J Algebra, 2013, 381: 233–259

11 SunJ. L-R-twisted tensor products of nonlocal vertex algebras and their modules. Comm Algebra (to appear)

12 SunJ. Twistors of nonlocal vertex algebras. Preprint

13 SunJ, YangH. Twisted tensor product modules for Möbius twisted tensor product nonlocal vertex algebras. Internat J Math, 2013, 24: 1350033

14 Van DaeleA, Van KeerS. The Yang-Baxter and pentagon equation. Compos Math, 1994, 91: 201–22