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Notes on Lie Algebras by Hans Samelson (English) Paperback Book
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Item specifics
- Condition
- Brand New: A new, unread, unused book in perfect condition with no missing or damaged pages. See all condition definitionsopens in a new window or tab
- ISBN-13
- 9780387972640
- Book Title
- Notes on Lie Algebras
- ISBN
- 9780387972640
- Subject Area
- Mathematics
- Publication Name
- Notes on Lie Algebras
- Item Length
- 9.3 in
- Publisher
- Springer New York
- Subject
- Group Theory, Algebra / Abstract, Topology
- Publication Year
- 1990
- Series
- Universitext Ser.
- Type
- Textbook
- Format
- Trade Paperback
- Language
- English
- Item Width
- 6.1 in
- Item Weight
- 9.8 Oz
- Number of Pages
- Xii, 162 Pages
About this product
Product Information
(Cartan sub Lie algebra, roots, Weyl group, Dynkin diagram, . . . ) and the classification, as found by Killing and Cartan (the list of all semisimple Lie algebras consists of (1) the special- linear ones, i. e. all matrices (of any fixed dimension) with trace 0, (2) the orthogonal ones, i. e. all skewsymmetric ma trices (of any fixed dimension), (3) the symplectic ones, i. e. all matrices M (of any fixed even dimension) that satisfy M J = - J MT with a certain non-degenerate skewsymmetric matrix J, and (4) five special Lie algebras G2, F , E , E , E , of dimensions 14,52,78,133,248, the "exceptional Lie 4 6 7 s algebras" , that just somehow appear in the process). There is also a discus sion of the compact form and other real forms of a (complex) semisimple Lie algebra, and a section on automorphisms. The third chapter brings the theory of the finite dimensional representations of a semisimple Lie alge bra, with the highest or extreme weight as central notion. The proof for the existence of representations is an ad hoc version of the present standard proof, but avoids explicit use of the Poincare-Birkhoff-Witt theorem. Complete reducibility is proved, as usual, with J. H. C. Whitehead's proof (the first proof, by H. Weyl, was analytical-topological and used the exis tence of a compact form of the group in question). Then come H.
Product Identifiers
Publisher
Springer New York
ISBN-10
0387972641
ISBN-13
9780387972640
eBay Product ID (ePID)
125590
Product Key Features
Publication Name
Notes on Lie Algebras
Format
Trade Paperback
Language
English
Subject
Group Theory, Algebra / Abstract, Topology
Publication Year
1990
Series
Universitext Ser.
Type
Textbook
Subject Area
Mathematics
Number of Pages
Xii, 162 Pages
Dimensions
Item Length
9.3 in
Item Width
6.1 in
Item Weight
9.8 Oz
Additional Product Features
Edition Number
2
Intended Audience
Scholarly & Professional
Number of Volumes
1 Vol.
Lc Classification Number
Qa252.3
Edition Description
Reprint,Revised Edition
Table of Content
1 Generalities.- 1.1 Basic definitions, examples.- 1.2 Structure constants.- 1.3 Relations with Lie groups.- 1.4 Elementary algebraic concepts.- 1.5 Representations; the Killing form.- 1.6 Solvable and nilpotent.- 1.7 Engel's theorem.- 1.8 Lie's theorem.- 1.9 Cartan's first criterion.- 1.10 Cartan's second criterion.- 1.11 Representations of A1.- 1.12 Complete reduction for A1.- 2 Structure Theory.- 2.1 Cartan subalgebra.- 2.2 Roots.- 2.3 Roots for semisimple g.- 2.4 Strings.- 2.5 Cartan integers.- 2.6 Root systems, Weyl group.- 2.7 Root systems of rank two.- 2.8 Weyl-Chevalley normal form, first stage.- 2.9 Weyl-Chevalley normal form.- 2.10 Compact form.- 2.11 Properties of root systems.- 2.12 Fundamental systems.- 2.13 Classification of fundamental systems.- 2.14 The simple Lie algebras.- 2.15 Automorphisms.- 3 Representations.- 3.1 The Cartan-Stiefel diagram.- 3.2 Weights and weight vectors.- 3.3 Uniqueness and existence.- 3.4 Complete reduction.- 3.5 Cartan semigroup; representation ring.- 3.6 The simple Lie algebras.- 3.7 The Weyl character formula.- 3.8 Some consequences of the character formula.- 3.9 Examples.- 3.10 The character ring.- 3.11 Orthogonal and symplectic representations.- References.- Symbol Index.
Copyright Date
1990
Dewey Decimal
512/.89
Dewey Edition
18
Illustrated
Yes
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