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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: Milne, J.S., 1942- Algebraic groups. Cambridge, United Kingdom ; New York, New York: Cambridge University Press, [2017] (OCoLC)992433996 |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
J S Milne |

ISBN: | 9781316711736 1316711730 |

OCLC Number: | 1004615128 |

Description: | 1 online resource (xiv, 644 pages) : illustrations |

Contents: | Definitions and basic properties -- Examples and basic constructions -- Affine algebraic groups and Hopf algebras -- Linear representations of algebraic groups -- Group theory: the isomorphism theorems -- Subnormal series; solvable and nilpotent algebraic groups -- Algebraic groups acting on schemes -- The structure of general algebraic groups -- The structure of general algebraic groups -- Tannaka duality; Jordan decompositions -- The Lie algebra of an algebraic group -- Finite group schemes -- Groups of multiplicative type; linearly reductive groups -- Tori acting on schemes -- Unipotent algebraic groups -- Cohomology and extensions -- The structure of solvable algebraic groups -- Borel subgroups and applications -- The geometry of algebraic groups -- Semisimple and reductive groups -- Algebraic groups of semisimple rank one -- Split reductive groups -- Representations of reductive groups -- The isogeny and existence theorems -- Construction of the semisimple groups -- Additional topics. |

Series Title: | Cambridge studies in advanced mathematics, 170. |

Responsibility: | J.S. Milne, University of Michigan, Ann Arbor. |

### Abstract:

## Reviews

*Editorial reviews*

Publisher Synopsis

'All together, this excellent text fills a long-standing gap in the textbook literature on algebraic groups. It presents the modern theory of group schemes in a very comprehensive, systematic, detailed and lucid manner, with numerous illustrating examples and exercises. It is fair to say that this reader-friendly textbook on algebraic groups is the long-desired modern successor to the old, venerable standard primers ...' Werner Kleinert, zbMath 'The author invests quite a lot to make difficult things understandable, and as a result, it is a real pleasure to read the book. All in all, with no doubt, Milne's new book will remain for decades an indispensable source for everybody interested in algebraic groups.' Boris E. Kunyavskii, MathSciNet 'All together, this excellent text fills a long-standing gap in the textbook literature on algebraic groups. It presents the modern theory of group schemes in a very comprehensive, systematic, detailed and lucid manner, with numerous illustrating examples and exercises. It is fair to say that this reader-friendly textbook on algebraic groups is the long-desired modern successor to the old, venerable standard primers ...' Werner Kleinert, zbMath 'The author invests quite a lot to make difficult things understandable, and as a result, it is a real pleasure to read the book. All in all, with no doubt, Milne's new book will remain for decades an indispensable source for everybody interested in algebraic groups.' Boris E. Kunyavskii, MathSciNet Read more...

*User-contributed reviews*