This volume presents lecture notes based on the author's courses on Lie algebras and the solution of Hilbert's fifth problem. In chapter 1, "Lie Algebras," the structure theory of semi-simple Lie algebras in characteristic zero is presented, following the ideas of Killing and Cartan. Chapter 2, "The Structure of Locally Compact Groups," deals with the solution of Hilbert's fifth problem given by Gleason, Montgomery, and Zipplin in 1952.
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About the Author
Irving Kaplansky is Director Emeritus of the Mathematical Sciences Research Institute and George Herbert Mead Distinguished Professor Emeritus in the Department of Mathematics at the University of Chicago.
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First Sentence:
Our beginning point is the concept of a ring: a set with an addition and multiplication satisfying the usual axioms, except that there is no assumption of associativity or of a substitute for associativity. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
induced invariant form, vector product algebra, compact symmetric neighborhood, canonical neighborhood, characteristic subspaces, abelian ideal, solvable ideals, nilpotent subalgebra, algebraically closed field, closed normal subgroup, nilpotent ideal, projective representation, lie algebras, associative ring Key Phrases - Capitalized Phrases (CAPs): (learn more)
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Our beginning point is the concept of a ring: a set with an addition and multiplication satisfying the usual axioms, except that there is no assumption of associativity or of a substitute for associativity. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
induced invariant form, vector product algebra, compact symmetric neighborhood, canonical neighborhood, characteristic subspaces, abelian ideal, solvable ideals, nilpotent subalgebra, algebraically closed field, closed normal subgroup, nilpotent ideal, projective representation, lie algebras, associative ring Key Phrases - Capitalized Phrases (CAPs): (learn more)
Let the D-system New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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This book cites 19
books:
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29
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- Theory of Unitary Group Representation (Chicago Lectures in Mathematics) by George W. Mackey in Front Matter
- Abstract Lie Algebras by David J. Winter in Back Matter
- Fuchsian Groups (Chicago Lectures in Mathematics) by Svetlana Katok in Front Matter
- Commutative Rings by Irving Kaplansky in Front Matter
- Topological Transformation Groups by D. Montgomery in Back Matter
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- Harmonic Analysis and Partial Differential Equations: Essays in Honor of Alberto P. Calderon (Chicago Lectures in Mathematics) by Michael Christ in Front Matter
- Harmonic Analysis and Partial Differential Equations: Essays in Honor of Alberto P. Calderon (Chicago Lectures in Mathematics) by Michael Christ in Front Matter
- Fuchsian Groups (Chicago Lectures in Mathematics) by Svetlana Katok in Front Matter
- Dimension Theory in Dynamical Systems: Contemporary Views and Applications (Chicago Lectures in Mathematics) by Yakov B. Pesin in Front Matter
- Dimension Theory in Dynamical Systems: Contemporary Views and Applications (Chicago Lectures in Mathematics) by Yakov B. Pesin in Front Matter
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