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On abelian intertwining algebras and...

Guo, Hong.

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On abelian intertwining algebras and their modules.

Record Type:	Electronic resources : Monograph/item
Title/Author:	On abelian intertwining algebras and their modules./
Author:	Guo, Hong.
Description:	84 p.
Notes:	Source: Dissertation Abstracts International, Volume: 56-03, Section: B, page: 1465.
Contained By:	Dissertation Abstracts International56-03B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9524183

On abelian intertwining algebras and their modules.
Guo, Hong.

On abelian intertwining algebras and their modules. - 84 p.

Source: Dissertation Abstracts International, Volume: 56-03, Section: B, page: 1465.

Thesis (Ph.D.)--Rutgers The State University of New Jersey - New Brunswick, 1995.

Parts of the representation theory of vertex operator algebras are extended to abelian intertwining algebras, which have been studied by Dong and Lepowsky. The notion of module for an abelian intertwining algebra is defined, the basic properties of such modules are discussed and various useful reformulations of the axioms are given. In particular, it is shown that the Jacobi identity in the definition of module can be replaced by the generalized commutator relation and generalized associator relation, or equivalent duality properties--generalized rationality, generalized commutativity and generalized associativity. These duality properties are used to prove that the tensor product of modules for abelian intertwining algebras has a natural module structure for the tensor product algebra. This result is also shown directly, that is, the Jacobi identity is established on the tensor product of the modules directly. This proof is apparently new even in the special case of ordinary vertex operator algebras. Adjoint vertex operators are introduced and contragredient modules are constructed. In the case of a vertex algebra associated with an even lattice, the contragredient modules are proved to be isomorphic to well-known ones. Finally, the rationality of the vertex operator algebra associated with an even positive definite lattice is established, that is, it is shown that any module for this algebra is completely reducible.Subjects--Topical Terms:

515831
Mathematics.

On abelian intertwining algebras and their modules.
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008 130610s1995 eng d
035 $a (UnM)AAI9524183
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100 1 $a Guo, Hong. $3 1677414
245 1 0 $a On abelian intertwining algebras and their modules.
300 $a 84 p.
500 $a Source: Dissertation Abstracts International, Volume: 56-03, Section: B, page: 1465.
500 $a Director: James Lepowsky.
502 $a Thesis (Ph.D.)--Rutgers The State University of New Jersey - New Brunswick, 1995.
520 $a Parts of the representation theory of vertex operator algebras are extended to abelian intertwining algebras, which have been studied by Dong and Lepowsky. The notion of module for an abelian intertwining algebra is defined, the basic properties of such modules are discussed and various useful reformulations of the axioms are given. In particular, it is shown that the Jacobi identity in the definition of module can be replaced by the generalized commutator relation and generalized associator relation, or equivalent duality properties--generalized rationality, generalized commutativity and generalized associativity. These duality properties are used to prove that the tensor product of modules for abelian intertwining algebras has a natural module structure for the tensor product algebra. This result is also shown directly, that is, the Jacobi identity is established on the tensor product of the modules directly. This proof is apparently new even in the special case of ordinary vertex operator algebras. Adjoint vertex operators are introduced and contragredient modules are constructed. In the case of a vertex algebra associated with an even lattice, the contragredient modules are proved to be isomorphic to well-known ones. Finally, the rationality of the vertex operator algebra associated with an even positive definite lattice is established, that is, it is shown that any module for this algebra is completely reducible.
590 $a School code: 0190.
650 4 $a Mathematics. $3 515831
690 $a 0405
710 2 0 $a Rutgers The State University of New Jersey - New Brunswick. $3 1017590
773 0 $t Dissertation Abstracts International $g 56-03B.
790 1 0 $a Lepowsky, James, $e advisor
790 $a 0190
791 $a Ph.D.
792 $a 1995
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9524183