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|a 9780817681869
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|a 10.1007/978-0-8176-8186-9
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| 100 |
1 |
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|a Lepowsky, James.
|e author.
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
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| 245 |
1 |
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|a Introduction to Vertex Operator Algebras and Their Representations
|h [electronic resource] /
|c by James Lepowsky, Haisheng Li.
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| 250 |
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|a 1st ed. 2004.
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| 264 |
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1 |
|a Boston, MA :
|b Birkhäuser Boston :
|b Imprint: Birkhäuser,
|c 2004.
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| 300 |
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|a XIII, 318 p.
|b online resource.
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| 490 |
1 |
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|a Progress in Mathematics,
|x 0743-1643 ;
|v 227
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| 490 |
1 |
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|a Springer eBook Collection
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| 505 |
0 |
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|a 1 Introduction -- 1.1 Motivation -- 1.2 Example of a vertex operator -- 1.3 The notion of vertex operator algebra -- 1.4 Simplification of the definition -- 1.5 Representations and modules -- 1.6 Construction of families of examples -- 1.7 Some further developments -- 2 Formal Calculus -- 2.1 Formal series and the formal delta function -- 2.2 Derivations and the formal Taylor Theorem -- 2.3 Expansions of zero and applications -- 3 Vertex Operator Algebras: The Axiomatic Basics -- 3.1 Definitions and some fundamental properties -- 3.2 Commutativity properties -- 3.3 Associativity properties -- 3.4 The Jacobi identity from commutativity and associativity -- 3.5 The Jacobi identity from commutativity -- 3.6 The Jacobi identity from skew symmetry and associativity -- 3.7 S3-symmetry of the Jacobi identity -- 3.8 The iterate formula and normal-ordered products -- 3.9 Further elementary notions -- 3.10 Weak nilpotence and nilpotence -- 3.11 Centralizers and the center -- 3.12 Direct product and tensor product vertex algebras -- 4 Modules -- 4.1 Definition and some consequences -- 4.2 Commutativity properties -- 4.3 Associativity properties -- 4.4 The Jacobi identity as a consequence of associativity and commutativity properties -- 4.5 Further elementary notions -- 4.6 Tensor product modules for tensor product vertex algebras -- 4.7 Vacuum-like vectors -- 4.8 Adjoining a module to a vertex algebra -- 5 Representations of Vertex Algebras and the Construction of Vertex Algebras and Modules -- 5.1 Weak vertex operators -- 5.2 The action of weak vertex operators on the space of weak vertex operators -- 5.3 The canonical weak vertex algebra ?(W) and the equivalence between modules and representations -- 5.4 Subalgebras of ?(W) -- 5.5 Local subalgebras and vertex subalgebras of ?(W) -- 5.6 Vertex subalgebras of ?(W) associated with the Virasoro algebra -- 5.7 General construction theorems for vertex algebras and modules -- 6 Construction of Families of Vertex Operator Algebras and Modules -- 6.1 Vertex operator algebras and modules associated to the Virasoro algebra -- 6.2 Vertex operator algebras and modules associated to affine Lie algebras -- 6.3 Vertex operator algebras and modules associated to Heisenberg algebras -- 6.4 Vertex operator algebras and modules associated to even lattices—the setting -- 6.5 Vertex operator algebras and modules associated to even lattices—the main results -- 6.6 Classification of the irreducible L?(?, O)-modules for g finite-dimensional simple and ? a positive integer -- References.
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|a Loaded electronically.
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| 590 |
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|a Electronic access restricted to members of the Holy Cross Community.
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| 650 |
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0 |
|a Algebra.
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| 650 |
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|a Associative rings.
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| 650 |
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|a Rings (Algebra).
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| 650 |
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|a Operator theory.
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| 650 |
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|a Topological groups.
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| 650 |
|
0 |
|a Lie groups.
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| 650 |
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0 |
|a Mathematical physics.
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| 690 |
|
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|a Electronic resources (E-books)
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| 700 |
1 |
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|a Li, Haisheng.
|e author.
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
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| 710 |
2 |
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|a SpringerLink (Online service)
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| 773 |
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| 830 |
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|a Progress in Mathematics,
|x 0743-1643 ;
|v 227
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| 830 |
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|a Springer eBook Collection.
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| 856 |
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|u https://holycross.idm.oclc.org/login?auth=cas&url=https://doi.org/10.1007/978-0-8176-8186-9
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