The Classical Groups: Their Invariants and Representations
by: Hermann Weyl
* Publisher: Princeton Univ Pr
* Number Of Pages: 336
* Publication Date: 1946-09
* Sales Rank: 2388078
* ISBN / ASIN: 0691079234
* EAN: 9780691079233
* Binding: Hardcover
* Manufacturer: Princeton Univ Pr
* Studio: Princeton Univ Pr
* Average Rating: 5
* Total Reviews: 2
Book Description:
In this renowned volume, Hermann Weyl discusses the symmetric, full linear, orthogonal, and symplectic groups and determines their different invariants and representations. Using basic concepts from algebra, he examines the various properties of the groups. Analysis and topology are used wherever appropriate. The book also covers topics such as matrix algebras, semigroups, commutators, and spinors, which are of great importance in understanding the group-theoretic structure of quantum mechanics.
Date: 2001-03-15 Rating: 5
Review:
Hard-core Group Theory
Forget about that pansy abstract axiom approach. This is the WWF of group theory. Weyl will take anyone to the mat with this book. It is packed with detail and demonstrations. He follows the vector space/matrix representation approach common to digital systems, physics and chemistry rather than axiomatic, generators/permutations approach more common in Abstract Algebra courses. This is the lineage that develops matrix transforms as groups starting from "the full group of all non-singular linear transformations and .. the orthogonal groups" (p. vii). The latter chapters cover characters and invariants. Galois and field theory have been vanquished. Chapter 2, "Remembrance of things past" is very entertaining. My favorite quote, "Here there is only one man to mention - Hilbert. His papers (1890/92) mark a turning point in the history of invariants theory. He solves the main problems and thus almost kills the whole subject." It's funny because it's true. This is almost a botanical treatise in which the matrix groups are studied as specimens in the jungle -- "...after all each group stands in its own right and does not deserve to be looked upon merely as a subgroup of...Her All-embracing Majesty GL(n)." (p 136). Historic references throughout provide motivation and entertainment. You couldn't possibly be disappointed with this book.
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