黎曼曲面上的流代数(英文版) 普通图书/自然科学 (俄罗斯)沙因曼世界图书出版公司 9787510076510

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作者: (俄罗斯)沙因曼
出版社: 世界图书出版公司
ISBN: 9787510076510

出版时间: 2017-01
装帧: 其他
开本: 其他

作者: (俄罗斯)沙因曼
出版社: 世界图书出版公司

ISBN: 9787510076510
出版时间: 2017-01

装帧: 其他
开本: 其他

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上书时间2023-06-20

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自然科学

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目录
1 Krichever-Novikov algebras: basic definitions and structure theory
  1.1 Current, vector field, and other Krichever-Novikov algebras
  1.2 Meromorphic λ-forms and Krichever-Novikov duality
  1.3 Krichever-Novikov bases
  1.4 Almost-graded structure, triangle decompositions
  1.5 Central extensions and 2-cohomology; Virasoro-type algebras
  1.6 Affine Krichever-Novikov, in particular Kac-Moody, algebras
  1.7 Central extensions of the Lie algebra □
  1.8 Local cocycles for sl(n) and gl(n)
2 Fermion representations and Sugawara construction
  2.1 Admissible representations and holomorphic bundles
  2.2 Holomorphic bundles in the Tyurin parametrization
  2.3 Krichever-Novikov bases for holomorphic vector bundles
  2.4 Fermion representations of affine algebras
  2.5 Verma modules for affine algebras
  2.6 Fermion representations of Virasoro-type algebras
  2.7 Sugawara representation
  2.8 Proof of the main theorems for the Sugawara construction
    2.8.1 Main theorems in the form of relations with structure constants
    2.8.2 End of the proof of the main theorems
3 Projective fiat connections on the moduli space of punctured Riemann
  surfaces and the Knizhnik-Zamolodchikov equation
  3.1 Virasoro-type algebras and moduli spaces of Riemann surfaces
  3.2 Sheaf of conformal blocks and other sheaves on the moduli space □
  3.3 Differentiation of the Krichever-Novikov objects in modular variables
3.4 Projective flat connection and generalized Knizhnik-Zamolodchikov equation
  3.5 Explicit form of the Knizhnik-Zamolodchikov equations for genus 0 and genus 1
    3.5.1 Explicit form of the equations for g = 0
    3.5.2 Explicit form of the equations for g = 1
  3.6 Appendix: the Krichever-Novikov base in the elliptic case
4 Lax operator algebras
  4.1 Lax operators and their Lie bracket
    4.1.1 Lax operator algebras for g1(n) and s1(n)
    4.1.2 Lax operator algebras for so(n)
    4.1.3 Lax operator algebras for sp(2n)
  4.2 Almost-graded structure
  4.3 Central extensions of Lax operator algebras: the construction
  4.4 Uniqueness theorem
5 Lax equations on Riemann surfaces, and their hierarchies
  5.1 M-operators
  5.2 L-operators and Lax operator algebras from M-operators
  5.3 α-valued Lax equations
  5.4 Hierarchies of commuting flows
  5.5 Symplectic structure
  5.6 Hamiltonian theory
  5.7 Examples: Calogero-Moser systems
6 Lax integrable systems and conformal field theory
  6.1 Conformal field theory related to a Lax integrable system
  6.2 From Lax operator algebra to commutative Krichever-Novikov algebra
  6.3 The representation of AL
  6.4 Sugawara representation
  6.5 Conformal blocks and the Knizhnik-Zamolodchikov connection
  6.6 The representation of the algebra of Hamiltonian vector fields and commuting Hamiltonians
  6.7 Unitarity
  6.8 Relation to geometric quantization and quantum integrable systems
  6.9 Remark on the Seiberg-Witten theory
Bibliography
Notation
Index

内容摘要
沙因曼著的《黎曼曲面上的流代数》介绍无穷界面代数理论及其进展，主要包括Krichever-Novikon代数理论的自相容展示，Lax算子代数，表象理论。
基于上述的黎曼曲面和全纯向量束的模块空间和Lax可积系和共型场论与上述理论之间联系。本书为初学者加入这一领域提供了一个契机。
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