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AuthorBiaล{130}ynicki-Birula, Andrzej. author
TitleAlgebraic Quotients. Torus Actions and Cohomology. The Adjoint Representation and the Adjoint Action [electronic resource] / by Andrzej Biaล{130}ynicki-Birula, James B. Carrell, William M. McGovern
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002
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Descript V, 242 p. online resource


This is the second volume of the new subseries "Invariant Theory and Algebraic Transformation Groups". The aim of the survey by A. Bialynicki-Birula is to present the main trends and achievements of research in the theory of quotients by actions of algebraic groups. This theory contains geometric invariant theory with various applications to problems of moduli theory. The contribution by J. Carrell treats the subject of torus actions on algebraic varieties, giving a detailed exposition of many of the cohomological results one obtains from having a torus action with fixed points. Many examples, such as toric varieties and flag varieties, are discussed in detail. W.M. McGovern studies the actions of a semisimple Lie or algebraic group on its Lie algebra via the adjoint action and on itself via conjugation. His contribution focuses primarily on nilpotent orbits that have found the widest application to representation theory in the last thirty-five years


I. Quotients by Actions of Groups -- II. Torus Actions and Cohomology -- III. The Adjoint Representation and the Adjoint Action

Mathematics Algebraic geometry Topological groups Lie groups Differential geometry Physics Mathematics Topological Groups Lie Groups Differential Geometry Algebraic Geometry Mathematical Methods in Physics


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