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AuthorTamanoi, Hirotaka. author
TitleElliptic Genera and Vertex Operator Super-Algebras [electronic resource] / by Hirotaka Tamanoi
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1999
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Descript VIII, 396 p. online resource


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 Kรคhler manifolds such as Riemannian tensors and Kรคhler 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


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 Kรคhler manifolds

Mathematics Algebra Nonassociative rings Rings (Algebra) Algebraic topology Physics Mathematics Algebra Algebraic Topology Non-associative Rings and Algebras Theoretical Mathematical and Computational Physics


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