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	On axiomatic approaches to intertwining operator algebras
	Chen, Ling1,2
刊名	Communications in contemporary mathematics
	2016-08-01
卷号	18期号:4页码:62
关键词	Intertwining operator algebras Moore-seiberg equations Jacobi identity Duality Locality
ISSN号	0219-1997
DOI	10.1142/s0219199715500510
通讯作者	Chen, ling(chenling2013@ucas.ac.cn)
英文摘要	We study intertwining operator algebras introduced and constructed by huang. in the case that the intertwining operator algebras involve intertwining operators among irreducible modules for their vertex operator subalgebras, a number of results on intertwining operator algebras were given in [y.-z. huang, generalized rationality and a "jacobi identity" for intertwining operator algebras, selecta math. (n.s.) 6 (2000) 225-267] but some of the proofs were postponed to an unpublished monograph. in this paper, we give the proofs of these results in [y.-z. huang, generalized rationality and a "jacobi identity" for intertwining operator algebras, selecta math. (n.s.) 6 (2000) 225-267] and we formulate and prove results for general intertwining operator algebras without assuming that the modules involved are irreducible. in particular, we construct fusing and braiding isomorphisms for general intertwining operator algebras and prove that they satisfy the genus-zero moore-seiberg equations. we show that the jacobi identity for intertwining operator algebras is equivalent to generalized rationality, commutativity and associativity properties of intertwining operator algebras. we introduce the locality for intertwining operator algebras and show that the jacobi identity is equivalent to the locality, assuming that other axioms hold. moreover, we establish that any two of the three properties, associativity, commutativity and skew-symmetry, imply the other (except that when deriving skew-symmetry from associativity and commutativity, more conditions are needed). finally, we show that three definitions of intertwining operator algebras are equivalent.
WOS关键词	CONFORMAL FIELD-THEORY ; MODULE CATEGORIES ; TENSOR-PRODUCTS ; VERTEX ALGEBRAS
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
语种	英语
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
WOS记录号	WOS:000381203200004
内容类型	期刊论文
URI标识	http://www.corc.org.cn/handle/1471x/2376359
专题	中国科学院大学
通讯作者	Chen, Ling
作者单位	1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Peking Univ, Beijing Int Ctr Math Res, Beijing 100871, Peoples R China
推荐引用方式 GB/T 7714	Chen, Ling. On axiomatic approaches to intertwining operator algebras[J]. Communications in contemporary mathematics,2016,18(4):62.
APA	Chen, Ling.(2016).On axiomatic approaches to intertwining operator algebras.Communications in contemporary mathematics,18(4),62.
MLA	Chen, Ling."On axiomatic approaches to intertwining operator algebras".Communications in contemporary mathematics 18.4(2016):62.

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