Enveloping Algebras (Graduate Studies in Mathematics)

Enveloping Algebras (Graduate Studies in Mathematics)

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  • 製本 Hardcover:ハードカバー版／ページ数 379 p.
  • 言語 ENG
  • 商品コード 9780821805602
  • DDC分類 512.24

Full Description

This book, which is the first systematic exposition of the algebraic approach to representations of Lie groups via representations of (or modules over) the corresponding universal enveloping algebras, turned out to be so well written that even today it remains one of the main textbooks and reference books on the subject. In 1992, Jacques Dixmier was awarded the Leroy P. Steele Prize for expository writing in mathematics. The Committee's citation mentioned ""Enveloping Algebras"" as one of Dixmier's 'extraordinary books'. Written with unique precision and elegance, the book provides the reader with insight and understanding of this very important subject. It can be an excellent textbook for a graduate course, as well as a very useful source of references in the theory of universal enveloping algebras, the area of mathematics that remains as important today as it was 20 years ago. For the 1996 printing the author updated the status of open problems and added some relevant references.

Contents

Lie algebras Enveloping algebras Two-sided ideals in enveloping algebras Centres Induced representations Primitive ideals (the solvable case) Verma modules The enveloping algebra of a semi-simple Lie algebra Harish-Chandra modules Primitive ideals (the general case) Appendix Problems Bibliography Added in 1996 Index.