《Emergence of the Theory of Lie Groupsl》是2000年Springer出版社出版的圖書。
基本介紹
- 中文名：Emergence of the Theory of Lie Groups
- 裝幀：Hardcover
- 定價：USD 99.00
- 作者：Thomas Hawkins
- 出版社：Springer
- 出版日期：2000年07月19日
- ISBN：9780387989631
媒體推薦,作者簡介,目錄,
媒體推薦
"....this study is just as clearly a stunning achievement. Few historians of mathematics have made a serious attempt to cross the bridge joining the nineteenth and twentieth centuries, and those who have made the journey have tended to avert their eyes from the mainstream traffic....the single greatest merit of Hawkins' book is that the author tries to place the reader in the middle of the action, offering a close up look at how mathematics gets made...Hawkins' account of this strange but wonderful saga resurrects a heroic chapter in the history of mathematics. For anyone with a serious interest in the rich background developments that led to modern Lie theory, this book should be browsed, read, savored, and read again."
-Notices of the AMS
作者簡介
Thomas Hawkins is co-pastor with his wife, Jan, at First Presbyterian Church in Charleston, Illinois. Prior to this pastorate, Hawkins was professor in the Career and Organizational Studies Program, Lumpkin College of Business and Applied Sciences at Eastern Illinois University. He is the author of several books published by Discipleship Resources, including
目錄
I: Sophus Lie.- 1. The Geometrical Origins of Lie’s Theory.- 1.1. Tetrahedral Line Complexes.- 1.2. W-Curves and W-Surfaces.- 1.3. Lie’s Idée Fixe.- 1.4. The Sphere Mapping.- 1.5. The Erlanger Programm.- 2. Jacobi and the Analytical Origins of Lie’s Theory.- 2.1. Jacobi’s Two Methods.- 2.2. The Calculus of Infinitesimal Transformations.- 2.3. Function Groups.- 2.4. The Invariant Theory of Contact Transformations.- 2.5. The Birth of Lie’s Theory of Groups.- 3. Lie’s Theory of Transformation Groups 1874–1893..- 3.1. The Group Classification Problem.- 3.2. An Overview of Lie’s Theory.- 3.3. The Adjoint Group.- 3.4. Complete Systems and Lie’s Idée Fixe.- 3.5. The Symplectic Groups.- II: Wilhelm Killing.- 4. The Background to Killing’s Work on Lie Algebras.- 4.1. Non-Euclidean Geometry and Weierstrassian Mathematics.- 4.2. Student Years in Berlin: 1867–1872.- 4.3. Non-Euclidean Geometry and General Space Forms.- 4.4. From Space Forms to Lie Algebras.- 4.5. Riemann and Helmholz.- 4.6. Killing and Klein on the Scope of Geometry.- ＞Chapter 5. Killing and the Structure of Lie Algebrass.- 5.1. Spaces Forms and Characteristic Equations.- 5.2. Encounter with Lie’s Theory.- 5.3. Correspondence with Engel.- 5.4. Killing’s Theory of Structure.- 5.5. Groups of Rank Zero.- 5.6. The Lobachevsky Prize.- III: Élie Cartan.- 6. The Doctoral Thesis of Élie Cartan.- 6.1. Lie and the Mathematicians of Paris.- 6.2. Cartan’s Theory of Semisimple Algebras.- 6.3. Killing’s Secondary Roots.- 6.4. Cartan’s Application of Secondary Roots.- 7. Lie’s School & Linear Representations.- 7.1. Representations in Lie’s Research Program.- 7.2. Eduard Study.- 7.3. Gino Fano.- 7.4. Cayley’s Counting Problem.- 7.5. Kowalewski’s Theory of Weights.- 8. Cartan’s Trilogy: 1913–14.- 8.1. Research Priorities 1893–1909.- 8.2. Another Application of Secondary Roots.- 8.3. Continuous Groups and Geometry.- 8.4. The Memoir of 1913.- 8.5. The Memoirs of 1914.- IV: Hermann Weyl.- 9. The Göttingen School of Hilbert.- 9.1. Hilbert and the Theory of Invariants.- 9.2. Hilbert at Göttingen.- 9.3. The Mathematization of Physics at Göttingen ..- 9.4. Weyl’s Göttingen Years: Integral Equations.- 9.5. Weyl’s Göttingen Years: Riemann Surfaces.- 9.6. Hilbert’s Brand of Mathematical Thinking.- 10. The Berlin Algebraists: Frobenius & Schur.- 10.1. Frobenius’ Theory of Group Characters & Representations.- 10.2. Hurwitz and the Theory of Invariants.- 10.3. Schur’s Doctoral Dissertation.- 10.4. Schur’s Career 1901–1923.- 10.5. Cayley’s Counting Problem Revisited.- 11. From Relativity to Representations.- 11.1. Einstein’s General Theory of Relativity.- 11.2. The Space Problem Reconsidered.- 11.3. Tensor Algebra & Tensor Symmetries.- 11.4. Weyl’s Response to Study.- 11.5. The Group-Theoretic Foundation of Tensor Calculus.- 12. Weyl’s Great Papers of 1925 and 1926.- 12.1. The Complete Reducibility Theorem.- 12.2. Schur and the Origins of Weyl’s 1925 Paper.- 12.3. Weyl’s Extension of the Killing-Cartan Theory.- 12.4. Weyl’s Finite Basis Theorem.- 12.5. Weyl’s Theory of Characters.- 12.6. Cartan’s Response.- 12.7. The Peter-Weyl Paper.- Afterword. Suggested Further Reading.- References. Published & Unpublished Sources.
