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Algebras of Virasoro type, Riemann surfaces and structures of the theory of solitons. (English. Russian original) Zbl 0634.17010
Funct. Anal. Appl. 21, No. 1-3, 126-142 (1987); translation from Funkts. Anal. Prilozh. 21, No. 2, 46-63 (1987).
From the text: “The goal of the present paper is the construction of regular analogs of Virasoro algebras and Verma modules, connected with nontrivial Riemann surfaces of genus \(g>0\). Although the goal cited is basic, we also consider briefly another physically important example of algebras, the current algebras. The concluding section of the paper is devoted to connection of this theory with the theory of solitons.”
Reviewer: Niels Jacob

MSC:
17B68 Virasoro and related algebras
14H55 Riemann surfaces; Weierstrass points; gap sequences
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
30F99 Riemann surfaces
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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