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Meromorphic open-string vertex algebras

### Abstract

A notion of meromorphic open-string vertex algebra is introduced. A meromorphic open-string vertex algebra is an open-string vertex algebra in the sense of Kong and the author satisfying additional rationality (or meromorphicity) conditions for vertex operators. The vertex operator map for a meromorphic open-string vertex algebra satisfies rationality and associativity but in general does not satisfy the Jacobi identity, commutativity, the commutator formula, the skew-symmetry or even the associator formula. Given a vector space , we construct a meromorphic open-string vertex algebra structure on the tensor algebra of the negative part of the affinization of such that the vertex algebra structure on the symmetric algebra of the negative part of the Heisenberg algebra associated to is a quotient of this meromorphic open-string vertex algebra. We also introduce the notion of left module for a meromorphic open-string vertex algebra and construct left modules for the meromorphic open-string vertex algebra above.

© 2013 AIP Publishing LLC

Received 16 May 2012
Accepted 30 April 2013
Published online 28 May 2013

Acknowledgments:
The author is supported in part by NSF (Grant No. PHY-0901237).

Article outline:

I. INTRODUCTION
II. DEFINITION OF MEROMORPHIC OPEN-STRING VERTEX ALGEBRA
III. A QUOTIENT ALGEBRA OF THE TENSOR ALGEBRA OF THE AFFINIZATION OF A VECTOR SPACE
IV. NORMAL ORDERING AND VERTEX OPERATORS
V. A MEROMORPHIC OPEN-STRING VERTEX ALGEBRASTRUCTURE ON
VI. LEFT MODULES FOR THE MEROMORPHIC OPEN-STRING VERTEX OPERATOR ALGEBRA

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2013-05-28

2016-09-25

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