# Essays in the History of Lie Groups and Algebraic Groups

## Borel, Armand

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Algebraic groups and Lie groups are important in most major areas of mathematics, occuring in diverse roles such as the symmetries of differential equations and as central figures in the Langlands program for number theory. In this book, Professor Borel looks at the development of the theory of Lie groups and algebraic groups, highlighting the evolution from the almost purely local theory at the start to the global theory that we know today. As the starting point of this passage from local to global, the author takes Lie's theory of local analytic transformation groups and Lie algebras. He then follows the globalization of the process in its two most important frameworks: (transcendental) differential geometry and algebraic geometry. Chapters II to IV are devoted to the former, Chapters V to VIII, to the latter.The essays in the first part of the book survey various proofs of the full reducibility of linear representations of $SL 2M$, the contributions H. Weyl to representation and invariant theory for Lie groups, and conclude with a chapter on E. Cartan's theory of symmetric spaces and Lie groups in the large. The second part of the book starts with Chapter V describing the development of the theory of linear algebraic groups in the 19th century. Many of the main contributions here are due to E. Study, E. Cartan, and above all, to L. Maurer. After being abandoned for nearly 50 years, the theory was revived by Chevalley and Kolchin and then further developed by many others. This is the focus of Chapter VI. The book concludes with two chapters on various aspects of the works of Chevalley on Lie groups and algebraic groups and Kolchin on algebraic groups and the Galois theory of differential fields. The author brings a unique perspective to this study. As an important developer of some of the modern elements of both the differential geometric and the algebraic geometric sides of the theory, he has a particularly deep appreciation of the underlying mathematics. His lifelong involvement and his historical research in the subject give him a special appreciation of the story of its development.

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## 1.Essays in the History of Lie Groups and Algebraic Groups (History of Mathematics, V. 21)

Editore: American Mathematical Society (2001)
ISBN 10: 0821802887 ISBN 13: 9780821802885
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Descrizione libro American Mathematical Society, 2001. Hardcover. Condizione libro: New. Brand new. We distribute directly for the publisher. Lie groups and algebraic groups are important in many major areas of mathematics and mathematical physics. We find them in diverse roles, notably as groups of automorphisms of geometric structures, as symmetries of differential systems, or as basic tools in the theory of automorphic forms. The author looks at their development, highlighting the evolution from the almost purely local theory at the start to the global theory that we know today. Starting from Lie's theory of local analytic transformation groups and early work on Lie algebras, he follows the process of globalization in its two main frameworks: differential geometry and topology on one hand, algebraic geometry on the other. Chapters II to IV are devoted to the former, Chapters V to VIII, to the latter.The essays in the first part of the book survey various proofs of the full reducibility of linear representations of $\mathbf{SL}_2{(\mathbb{C})}$, the contributions of H. Weyl to representations and invariant theory for semisimple Lie groups, and conclude with a chapter on E. Cartan's theory of symmetric spaces and Lie groups in the large.The second part of the book first outlines various contributions to linear algebraic groups in the 19th century, due mainly to E. Study, E. Picard, and above all, L. Maurer. After being abandoned for nearly fifty years, the theory was revived by C. Chevalley and E. Kolchin, and then further developed by many others. This is the focus of Chapter VI. The book concludes with two chapters on the work of Chevalley on Lie groups and Lie algebras and of Kolchin on algebraic groups and the Galois theory of differential fields, which put their contributions to algebraic groups in a broader context.Professor Borel brings a unique perspective to this study. As an important developer of some of the modern elements of both the differential geometric and the algebraic geometric sides of the theory, he has a particularly deep understanding of the underlying mathematics. His lifelong involvement and his historical research in the subject area give him a special appreciation of the story of its development.Co-published with the London Mathematical Society beginning with Volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners. Codice libro della libreria 1007150014

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## 2.Essays in the History of Lie Groups and Algebraic Groups (Hardback)

Editore: American Mathematical Society, United States (2001)
ISBN 10: 0821802887 ISBN 13: 9780821802885
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Descrizione libro American Mathematical Society, United States, 2001. Hardback. Condizione libro: New. 254 x 178 mm. Language: English . Brand New Book. Algebraic groups and Lie groups are important in most major areas of mathematics, occuring in diverse roles such as the symmetries of differential equations and as central figures in the Langlands program for number theory. In this book, Professor Borel looks at the development of the theory of Lie groups and algebraic groups, highlighting the evolution from the almost purely local theory at the start to the global theory that we know today. As the starting point of this passage from local to global, the author takes Lie s theory of local analytic transformation groups and Lie algebras. He then follows the globalization of the process in its two most important frameworks: (transcendental) differential geometry and algebraic geometry. Chapters II to IV are devoted to the former, Chapters V to VIII, to the latter.The essays in the first part of the book survey various proofs of the full reducibility of linear representations of $SL 2M$, the contributions H. Weyl to representation and invariant theory for Lie groups, and conclude with a chapter on E. Cartan s theory of symmetric spaces and Lie groups in the large. The second part of the book starts with Chapter V describing the development of the theory of linear algebraic groups in the 19th century. Many of the main contributions here are due to E. Study, E. Cartan, and above all, to L. Maurer. After being abandoned for nearly 50 years, the theory was revived by Chevalley and Kolchin and then further developed by many others. This is the focus of Chapter VI. The book concludes with two chapters on various aspects of the works of Chevalley on Lie groups and algebraic groups and Kolchin on algebraic groups and the Galois theory of differential fields. The author brings a unique perspective to this study. As an important developer of some of the modern elements of both the differential geometric and the algebraic geometric sides of the theory, he has a particularly deep appreciation of the underlying mathematics. His lifelong involvement and his historical research in the subject give him a special appreciation of the story of its development. Codice libro della libreria AAN9780821802885

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## 3.Essays in the History of Lie Groups and Algebraic Groups (Hardback)

Editore: American Mathematical Society, United States (2001)
ISBN 10: 0821802887 ISBN 13: 9780821802885
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Descrizione libro American Mathematical Society, United States, 2001. Hardback. Condizione libro: New. 254 x 178 mm. Language: English . Brand New Book. Algebraic groups and Lie groups are important in most major areas of mathematics, occuring in diverse roles such as the symmetries of differential equations and as central figures in the Langlands program for number theory. In this book, Professor Borel looks at the development of the theory of Lie groups and algebraic groups, highlighting the evolution from the almost purely local theory at the start to the global theory that we know today. As the starting point of this passage from local to global, the author takes Lie s theory of local analytic transformation groups and Lie algebras. He then follows the globalization of the process in its two most important frameworks: (transcendental) differential geometry and algebraic geometry. Chapters II to IV are devoted to the former, Chapters V to VIII, to the latter.The essays in the first part of the book survey various proofs of the full reducibility of linear representations of $SL 2M$, the contributions H. Weyl to representation and invariant theory for Lie groups, and conclude with a chapter on E. Cartan s theory of symmetric spaces and Lie groups in the large. The second part of the book starts with Chapter V describing the development of the theory of linear algebraic groups in the 19th century. Many of the main contributions here are due to E. Study, E. Cartan, and above all, to L. Maurer. After being abandoned for nearly 50 years, the theory was revived by Chevalley and Kolchin and then further developed by many others. This is the focus of Chapter VI. The book concludes with two chapters on various aspects of the works of Chevalley on Lie groups and algebraic groups and Kolchin on algebraic groups and the Galois theory of differential fields. The author brings a unique perspective to this study. As an important developer of some of the modern elements of both the differential geometric and the algebraic geometric sides of the theory, he has a particularly deep appreciation of the underlying mathematics. His lifelong involvement and his historical research in the subject give him a special appreciation of the story of its development. Codice libro della libreria AAN9780821802885

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## 4.Essays In The History Of Lie Groups And Algebraic Groups

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## 5.Essays in the History of Lie Groups and Algebraic Groups

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Descrizione libro American Mathematical Society. Hardback. Condizione libro: new. BRAND NEW, Essays in the History of Lie Groups and Algebraic Groups, Armand Borel, Algebraic groups and Lie groups are important in most major areas of mathematics, occuring in diverse roles such as the symmetries of differential equations and as central figures in the Langlands program for number theory. In this book, Professor Borel looks at the development of the theory of Lie groups and algebraic groups, highlighting the evolution from the almost purely local theory at the start to the global theory that we know today. As the starting point of this passage from local to global, the author takes Lie's theory of local analytic transformation groups and Lie algebras. He then follows the globalization of the process in its two most important frameworks: (transcendental) differential geometry and algebraic geometry. Chapters II to IV are devoted to the former, Chapters V to VIII, to the latter.The essays in the first part of the book survey various proofs of the full reducibility of linear representations of $SL 2M$, the contributions H. Weyl to representation and invariant theory for Lie groups, and conclude with a chapter on E. Cartan's theory of symmetric spaces and Lie groups in the large. The second part of the book starts with Chapter V describing the development of the theory of linear algebraic groups in the 19th century. Many of the main contributions here are due to E. Study, E. Cartan, and above all, to L. Maurer. After being abandoned for nearly 50 years, the theory was revived by Chevalley and Kolchin and then further developed by many others. This is the focus of Chapter VI. The book concludes with two chapters on various aspects of the works of Chevalley on Lie groups and algebraic groups and Kolchin on algebraic groups and the Galois theory of differential fields. The author brings a unique perspective to this study. As an important developer of some of the modern elements of both the differential geometric and the algebraic geometric sides of the theory, he has a particularly deep appreciation of the underlying mathematics. His lifelong involvement and his historical research in the subject give him a special appreciation of the story of its development. Codice libro della libreria B9780821802885

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## 6.Essays in the History of Lie Groups and Algebraic Groups

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Descrizione libro American Mathematical Society, 2001. HRD. Condizione libro: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Codice libro della libreria CE-9780821802885

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## 7.Essays in the History of Lie Groups and Algebraic Groups (History of Mathematics, V. 21)

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Descrizione libro American Mathematical Society, 2001. Hardcover. Condizione libro: New. book. Codice libro della libreria 0821802887

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## 8.Essays in the History of Lie Groups and Algebraic Groups (History of Mathematics, V. 21)

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Descrizione libro American Mathematical Society, 2001. Hardcover. Condizione libro: New. Codice libro della libreria DADAX0821802887

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## 9.Essays in the History of Lie Groups and Algebraic Groups (History of Mathematics, V. 21)

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Descrizione libro Amer Mathematical Society, 2001. Hardcover. Condizione libro: Brand New. 184 pages. 10.00x7.00x0.50 inches. In Stock. Codice libro della libreria __0821802887

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## 10.Essays in the History of Lie Groups and Algebraic Groups (Hardcover)

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Descrizione libro 2001. Hardcover. Condizione libro: New. 261mm x 184mm x. Hardcover. Algebraic groups and Lie groups are important in most major areas of mathematics, occuring in diverse roles such as the symmetries of differential equations and as central figures in the L.Shipping may be from multiple locations in the US or from the UK, depending on stock availability. 184 pages. 0.570. Codice libro della libreria 9780821802885

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