Virasoro algebra and Teichm�ller spaces
Copyright policy )Virasoro algebra and Teichm�ller spaces
It is shown that the set of equivalence classes of triples \((C,p,t)\), where \(C\) is a complex Riemann surface of genus \(g\), \(p\) a point of \(C\) and \(t\) an \(\infty\)-jet of a coordinate at \(p\) is infinitesimally a double coset space of the central extension of the group of diffeomorphisms of the circle (the Virasoro group) modulo analogues of a compact and a discrete subgroup and its embedding into an infinite dimensional Grassmannian is described. Fortunately, these results, discovered independently, are presented in more detailed and easier to read form in \textit{A. A. Beilinson} and \textit{V. V. Schechtman} [Commun. Math. Phys. 118, 651--701 (1988; Zbl 0665.17010)], \textit{B. Arbarello}, \textit{C. De Concini}, \textit{V. Kac} and \textit{C. Procesi}, Commun. Math. Phys. 117, No. 1, 1--36 (1988; Zbl 0647.17010)] and [\textit{N. Kawamoto, Y. Namikawa, A. Tsuchiya} and \textit{Y. Yamada}, Commun. Math. Phys. 116, No. 2, 247--308 (1988; Zbl 0648.35080)].
Virasoro algebra, Groups of diffeomorphisms and homeomorphisms as manifolds, Virasoro and related algebras, Infinite-dimensional Lie groups and their Lie algebras: general properties, Virasoro group, Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds, Teichmüller spaces
Virasoro algebra, Groups of diffeomorphisms and homeomorphisms as manifolds, Virasoro and related algebras, Infinite-dimensional Lie groups and their Lie algebras: general properties, Virasoro group, Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds, Teichmüller spaces
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