Elliptic Genera and Vertex Operator Super-Algebras
Tamanoi, Hirotaka.
Elliptic Genera and Vertex Operator Super-Algebras [electronic resource] / by Hirotaka Tamanoi. - VIII, 396 p. online resource. - Lecture Notes in Mathematics, 1704 0075-8434 ; . - Lecture Notes in Mathematics, 1704 .
and summary of results -- Elliptic genera -- Vertex operator super algebras -- G-invariant vertex operator super subalgebras -- Geometric structure in vector spaces and reduction of structure groups on manifolds -- Infinite dimensional symmetries in elliptic genera for Kähler manifolds.
This monograph deals with two aspects of the theory of elliptic genus: its topological aspect involving elliptic functions, and its representation theoretic aspect involving vertex operator super-algebras. For the second aspect, elliptic genera are shown to have the structure of modules over certain vertex operator super-algebras. The vertex operators corresponding to parallel tensor fields on closed Riemannian Spin Kähler manifolds such as Riemannian tensors and Kähler forms are shown to give rise to Virasoro algebras and affine Lie algebras. This monograph is chiefly intended for topologists and it includes accounts on topics outside of topology such as vertex operator algebras.
9783540487883
10.1007/BFb0092541 doi
Algebra.
Algebraic topology.
Algebra.
Algebraic Topology.
Non-associative Rings and Algebras.
Theoretical, Mathematical and Computational Physics.
QA150-272
512
Elliptic Genera and Vertex Operator Super-Algebras [electronic resource] / by Hirotaka Tamanoi. - VIII, 396 p. online resource. - Lecture Notes in Mathematics, 1704 0075-8434 ; . - Lecture Notes in Mathematics, 1704 .
and summary of results -- Elliptic genera -- Vertex operator super algebras -- G-invariant vertex operator super subalgebras -- Geometric structure in vector spaces and reduction of structure groups on manifolds -- Infinite dimensional symmetries in elliptic genera for Kähler manifolds.
This monograph deals with two aspects of the theory of elliptic genus: its topological aspect involving elliptic functions, and its representation theoretic aspect involving vertex operator super-algebras. For the second aspect, elliptic genera are shown to have the structure of modules over certain vertex operator super-algebras. The vertex operators corresponding to parallel tensor fields on closed Riemannian Spin Kähler manifolds such as Riemannian tensors and Kähler forms are shown to give rise to Virasoro algebras and affine Lie algebras. This monograph is chiefly intended for topologists and it includes accounts on topics outside of topology such as vertex operator algebras.
9783540487883
10.1007/BFb0092541 doi
Algebra.
Algebraic topology.
Algebra.
Algebraic Topology.
Non-associative Rings and Algebras.
Theoretical, Mathematical and Computational Physics.
QA150-272
512