The Resource Two-Dimensional Conformal Geometry and Vertex Operator Algebras, by Yi-Zhi Huang, (electronic resource)

Two-Dimensional Conformal Geometry and Vertex Operator Algebras, by Yi-Zhi Huang, (electronic resource)

Label
Two-Dimensional Conformal Geometry and Vertex Operator Algebras
Title
Two-Dimensional Conformal Geometry and Vertex Operator Algebras
Statement of responsibility
by Yi-Zhi Huang
Creator
Author
Author
Subject
Language
  • eng
  • eng
Member of
http://library.link/vocab/creatorName
Huang, Yi-Zhi
Dewey number
516.35
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
-5PW39lv9JE
Image bit depth
0
Language note
English
LC call number
QA564-609
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Progress in Mathematics,
Series volume
148
http://library.link/vocab/subjectName
  • Geometry, algebraic
  • Operator theory
  • Topological Groups
  • Mathematical physics
  • Geometry
  • Algebra
  • Algebraic Geometry
  • Operator Theory
  • Topological Groups, Lie Groups
  • Mathematical Methods in Physics
  • Geometry
  • Algebra
Label
Two-Dimensional Conformal Geometry and Vertex Operator Algebras, by Yi-Zhi Huang, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
Notational conventions -- 1. Spheres with tubes -- 1.1. Definitions -- 1.2. The sewing operation -- 1.3. The moduli spaces of spheres with tubes -- 1.4. The sewing equation -- 1.5. Meromorphic functions on the moduli spaces and meromorphic tangent spaces -- 2. Algebraic study of the sewing operation -- 2.1. Formal power series and exponentials of derivations -- 2.2. The formal sewing equation and the sewing identities -- 3. Geometric study of the sewing operation -- 3.1. Moduli spaces, meromorphic functions and meromorphic tangent spaces revisited -- 3.2. The sewing operation and spheres with tubes of type (1,0), (1,1) and (1,2) -- 3.3. Generalized spheres with tubes -- 3.4. The sewing formulas and the convergence of the associated series via the Fischer-Grauert Theorem -- 3.5. A Virasoro algebra structure of central charge 0 on the meromorphic tangent space of K(1) at its identity -- 4. Realizations of the sewing identities -- 4.1. The Virasoro algebra and modules -- 4.2. Realizations of the sewing identities for general representations of the Virasoro algebra -- 4.3. Realizations of the sewing identities for positive energy representations of the Virasoro algebra -- 5. Geometric vertex operator algebras -- 5.1. Linear algebra of graded vector spaces with finite-dimensional homogeneous subspaces -- 5.2. The notion of geometric vertex operator algebra -- 5.3. Vertex operator algebras -- 5.4. The isomorphism between the category of geometric vertex operator algebras and the category of vertex operator algebras -- 6. Vertex partial operads -- 6.1. The ?x -rescalable partial operad structure on the sequence K of moduli spaces -- 6.2. The topological and analytic structures on K -- 6.3. The associativity of the sphere partial operad K -- 6.4. Suboperads and partial suboperads of K -- 6.5. The determinant line bundles over K and the partial operad structure -- 6.6. Meromorphic tangent spaces of determinant line bundles and a module for the Virasoro algebra -- 6.7. Proof of the convergence of projective factors in the sewing axiom -- 6.8. Complex powers of the determinant line bundles -- 6.9. ?-extensions of K -- 7. The isomorphism theorem and applications -- 7.1. Vertex associative algebras -- 7.2. The isomorphism theorem -- 7.3. Geometric construction of some Virasoro vertex operator algebras -- 7.4. Isomorphic vertex operator algebras induced from conformal maps -- Appendix A. Answers to selected exercises -- A.1. Exercise 1.3.5: The proof of Proposition 1.3.4 -- A.2. Exercise 2.1.8: Another proof of Proposition 2.1.7 -- A.3. Exercise 2.1.12: The proof of Proposition 2.1.11 -- A.4. Exercise 2.1.17: The proof of Proposition 2.1.16 -- A.5. Exercise 2.1.20: The proof of Proposition 2.1.19 -- A.6. Exercise 3.4.2: The sewing formulas -- A.7. Exercise 3.5.1: The definition of the Virasoro bracket -- A.8. Exercise 3.5.3: The calculation of the Virasoro bracket -- A.10. Exercise 5.4.3: The proof of the formula (5.4.10) -- A.11. Exercise 6.6.3: The proof of the formula (6.6.20) -- A.12. Exercise 6.7.2: The proof of Lemma 6.7.1 -- Appendix B. (LB)-spaces and complex (LB)-manifolds -- Appendix C. Operads and partial operads -- C.1. Operads, partial operads and associated algebraic structures -- C.2. Rescaling groups for partial operads, rescalable partial operads and associated algebraic structures -- C.3. Another definition of (partial) operad -- Appendix D. Determinant lines and determinant line bundles -- D.1. Some classes of bounded linear operators -- D.2. Determinant lines -- D.3. Determinant lines over Riemann surfaces with parametrized boundaries -- D.4. Canonical isomorphisms associated to sewing and determinant line bundles over moduli spaces -- D.6. One-dimensional genus-zero modular functors and the Mumford-Segal theorem
Dimensions
unknown
Edition
1st ed. 1997.
Extent
1 online resource (XIV, 282 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461242765
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-1-4612-4276-5
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000090781
  • (SSID)ssj0001298866
  • (PQKBManifestationID)11842447
  • (PQKBTitleCode)TC0001298866
  • (PQKBWorkID)11261837
  • (PQKB)11289618
  • (DE-He213)978-1-4612-4276-5
  • (MiAaPQ)EBC3076099
  • (EXLCZ)993400000000090781
Label
Two-Dimensional Conformal Geometry and Vertex Operator Algebras, by Yi-Zhi Huang, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
Notational conventions -- 1. Spheres with tubes -- 1.1. Definitions -- 1.2. The sewing operation -- 1.3. The moduli spaces of spheres with tubes -- 1.4. The sewing equation -- 1.5. Meromorphic functions on the moduli spaces and meromorphic tangent spaces -- 2. Algebraic study of the sewing operation -- 2.1. Formal power series and exponentials of derivations -- 2.2. The formal sewing equation and the sewing identities -- 3. Geometric study of the sewing operation -- 3.1. Moduli spaces, meromorphic functions and meromorphic tangent spaces revisited -- 3.2. The sewing operation and spheres with tubes of type (1,0), (1,1) and (1,2) -- 3.3. Generalized spheres with tubes -- 3.4. The sewing formulas and the convergence of the associated series via the Fischer-Grauert Theorem -- 3.5. A Virasoro algebra structure of central charge 0 on the meromorphic tangent space of K(1) at its identity -- 4. Realizations of the sewing identities -- 4.1. The Virasoro algebra and modules -- 4.2. Realizations of the sewing identities for general representations of the Virasoro algebra -- 4.3. Realizations of the sewing identities for positive energy representations of the Virasoro algebra -- 5. Geometric vertex operator algebras -- 5.1. Linear algebra of graded vector spaces with finite-dimensional homogeneous subspaces -- 5.2. The notion of geometric vertex operator algebra -- 5.3. Vertex operator algebras -- 5.4. The isomorphism between the category of geometric vertex operator algebras and the category of vertex operator algebras -- 6. Vertex partial operads -- 6.1. The ?x -rescalable partial operad structure on the sequence K of moduli spaces -- 6.2. The topological and analytic structures on K -- 6.3. The associativity of the sphere partial operad K -- 6.4. Suboperads and partial suboperads of K -- 6.5. The determinant line bundles over K and the partial operad structure -- 6.6. Meromorphic tangent spaces of determinant line bundles and a module for the Virasoro algebra -- 6.7. Proof of the convergence of projective factors in the sewing axiom -- 6.8. Complex powers of the determinant line bundles -- 6.9. ?-extensions of K -- 7. The isomorphism theorem and applications -- 7.1. Vertex associative algebras -- 7.2. The isomorphism theorem -- 7.3. Geometric construction of some Virasoro vertex operator algebras -- 7.4. Isomorphic vertex operator algebras induced from conformal maps -- Appendix A. Answers to selected exercises -- A.1. Exercise 1.3.5: The proof of Proposition 1.3.4 -- A.2. Exercise 2.1.8: Another proof of Proposition 2.1.7 -- A.3. Exercise 2.1.12: The proof of Proposition 2.1.11 -- A.4. Exercise 2.1.17: The proof of Proposition 2.1.16 -- A.5. Exercise 2.1.20: The proof of Proposition 2.1.19 -- A.6. Exercise 3.4.2: The sewing formulas -- A.7. Exercise 3.5.1: The definition of the Virasoro bracket -- A.8. Exercise 3.5.3: The calculation of the Virasoro bracket -- A.10. Exercise 5.4.3: The proof of the formula (5.4.10) -- A.11. Exercise 6.6.3: The proof of the formula (6.6.20) -- A.12. Exercise 6.7.2: The proof of Lemma 6.7.1 -- Appendix B. (LB)-spaces and complex (LB)-manifolds -- Appendix C. Operads and partial operads -- C.1. Operads, partial operads and associated algebraic structures -- C.2. Rescaling groups for partial operads, rescalable partial operads and associated algebraic structures -- C.3. Another definition of (partial) operad -- Appendix D. Determinant lines and determinant line bundles -- D.1. Some classes of bounded linear operators -- D.2. Determinant lines -- D.3. Determinant lines over Riemann surfaces with parametrized boundaries -- D.4. Canonical isomorphisms associated to sewing and determinant line bundles over moduli spaces -- D.6. One-dimensional genus-zero modular functors and the Mumford-Segal theorem
Dimensions
unknown
Edition
1st ed. 1997.
Extent
1 online resource (XIV, 282 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461242765
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-1-4612-4276-5
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000090781
  • (SSID)ssj0001298866
  • (PQKBManifestationID)11842447
  • (PQKBTitleCode)TC0001298866
  • (PQKBWorkID)11261837
  • (PQKB)11289618
  • (DE-He213)978-1-4612-4276-5
  • (MiAaPQ)EBC3076099
  • (EXLCZ)993400000000090781

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