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Classic Reviews in Mathematics and Mathematical Physics

Classic Reviews in Mathematics and Mathematical Physics

Edited by I.M.Krichever


The review papers in this series were originally published in English in the 1980s and were written by the very best Soviet experts and are now acknowledged as classic papers in particular areas of mathematics and physics. Written as front line reviews, many of these papers could be used as reference books for the modern generation of students and researchers. The lack of corresponding literature and ever growing interest in theoretical and mathematical physics and the remarkable results of recent years in soliton theory, the theory of quantum topological model and their applications in topology, algebraic and differential geometry are the main reasons for publishing this series of updated and annotated editions of these classic papers.

Triangle Equations and Simple Lie Algebras 
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Hb       100pp      1998


A.A.Belavin, L.D.Landau Institute for Theoretical Physics, Moscow, Russia

V.G.Drinfeld, Physical-Technical Institute of Low Temperatures, Kharkov, Ukraine


This classic paper pertaining to the theory of the Yang-Baxter equations presents results on the applications of methods of the theory of Lie algebras to the classification of solutions of the Yang-Baxter equations.


Topological and Algebraic Geometry Methods in Contemporary Mathematical Physics 
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Hb       200pp     2004

B.A.Dubrovin, International School for Advanced Studies, Trieste, Italy

I.M.Krichever, S.P.Novikov, L.D.Landau Institute of Theoretical Physics, Moscow, Russia


This volume is a classic survey of algebraic geometry and topological methods in various problems of mathematical physics and provides an excellent reference text for graduate students and researchers. The book is divided into three parts: the first part concerns Hamiltonian formalism and methods that generalise Morse for certain dynamical systems of physical origin: the second part presents algebraic geometry analysis of the Yang-Baxter equations for two-dimensional models: and finally part three presents the theory of multidimensional theta functions of Abel, Riemann, Poincare in a form that is elementally and convenient for applications.


Geometric Integration Theory on Supermanifolds 
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T.Voronov , University of Manchester, UK

2012    150pp    Hb

This volume provides a detailed account of the theory of forms on supermanifolds a correct and non-trivial analogue of Cartan-de Rham theory based on new concepts. The apparatus of supermanifold differential topology necessary for the integration theory is developed. A key feature is the identification of a class of proper morphisms intimately connected with Berezin integration, which are of fundamental importance in various problems. The work also contains a condensed introduction to superanalysis and supermanifolds, free from algebraic formalism which sets out afresh such challenging problems as the Berezin integral on a bounded domain. The volume includes an Appendix to present a current perspective on the original survey and provides an excellent reference text for graduate students and researchers.


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