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Synopsis
Ah Love! Could you and I with Him consl?ire To grasp this sorry Scheme of things entIre' KHAYYAM People investigating algebraic groups have studied the same objects in many different guises. My first goal thus has been to take three different viewpoints and demonstrate how they offer complementary intuitive insight into the subject. In Part I we begin with a functorial idea, discussing some familiar processes for constructing groups. These turn out to be equivalent to the ring-theoretic objects called Hopf algebras, with which we can then con struct new examples. Study of their representations shows that they are closely related to groups of matrices, and closed sets in matrix space give us a geometric picture of some of the objects involved. This interplay of methods continues as we turn to specific results. In Part II, a geometric idea (connectedness) and one from classical matrix theory (Jordan decomposition) blend with the study of separable algebras. In Part III, a notion of differential prompted by the theory of Lie groups is used to prove the absence of nilpotents in certain Hopf algebras. The ring-theoretic work on faithful flatness in Part IV turns out to give the true explanation for the behavior of quotient group functors. Finally, the material is connected with other parts of algebra in Part V, which shows how twisted forms of any algebraic structure are governed by its automorphism group scheme.
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- PublisherSpringer
- Publication date1979
- ISBN 10 0387904212
- ISBN 13 9780387904214
- BindingHardcover
- LanguageEnglish
- Number of pages176
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Introduction to Affine Group Schemes (Graduate Texts in Mathematics, 66)
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Introduction to Affine Group Schemes
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ISBN 10: 0387904212
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Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Ah Love! Could you and I with Him consl ire To grasp this sorry Scheme of things entIre' KHAYYAM People investigating algebraic groups have studied the same objects in many different guises. My first goal thus has been to take three different viewpoints and demonstrate how they offer complementary intuitive insight into the subject. In Part I we begin with a functorial idea, discussing some familiar processes for constructing groups. These turn out to be equivalent to the ring-theoretic objects called Hopf algebras, with which we can then con struct new examples. Study of their representations shows that they are closely related to groups of matrices, and closed sets in matrix space give us a geometric picture of some of the objects involved. This interplay of methods continues as we turn to specific results. In Part II, a geometric idea (connectedness) and one from classical matrix theory (Jordan decomposition) blend with the study of separable algebras. In Part III, a notion of differential prompted by the theory of Lie groups is used to prove the absence of nilpotents in certain Hopf algebras. The ring-theoretic work on faithful flatness in Part IV turns out to give the true explanation for the behavior of quotient group functors. Finally, the material is connected with other parts of algebra in Part V, which shows how twisted forms of any algebraic structure are governed by its automorphism group scheme. 180 pp. Englisch. Seller Inventory # 9780387904214
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Introduction to affine group schemes. Graduate texts in mathematics
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Introduction to Affine Group Schemes
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Introduction to Affine Group Schemes
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Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - Ah Love! Could you and I with Him consl ire To grasp this sorry Scheme of things entIre' KHAYYAM People investigating algebraic groups have studied the same objects in many different guises. My first goal thus has been to take three different viewpoints and demonstrate how they offer complementary intuitive insight into the subject. In Part I we begin with a functorial idea, discussing some familiar processes for constructing groups. These turn out to be equivalent to the ring-theoretic objects called Hopf algebras, with which we can then con struct new examples. Study of their representations shows that they are closely related to groups of matrices, and closed sets in matrix space give us a geometric picture of some of the objects involved. This interplay of methods continues as we turn to specific results. In Part II, a geometric idea (connectedness) and one from classical matrix theory (Jordan decomposition) blend with the study of separable algebras. In Part III, a notion of differential prompted by the theory of Lie groups is used to prove the absence of nilpotents in certain Hopf algebras. The ring-theoretic work on faithful flatness in Part IV turns out to give the true explanation for the behavior of quotient group functors. Finally, the material is connected with other parts of algebra in Part V, which shows how twisted forms of any algebraic structure are governed by its automorphism group scheme. Seller Inventory # 9780387904214
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Introduction to Affine Group Schemes
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Introduction to Affine Group Schemes (Graduate Texts in Mathematics, 66)
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