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AuthorHuang, Yi-Zhi. author
TitleTwo-Dimensional Conformal Geometry and Vertex Operator Algebras [electronic resource] / by Yi-Zhi Huang
ImprintBoston, MA : Birkhรคuser Boston, 1997
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Descript XIV, 282 p. online resource


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

Mathematics Algebra Algebraic geometry Topological groups Lie groups Operator theory Geometry Physics Mathematics Algebraic Geometry Operator Theory Topological Groups Lie Groups Mathematical Methods in Physics Geometry Algebra


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