| dc.description.abstract | The primary goal of these lectures is to introduce a beginner to the finitedimensional
representations of Lie groups and Lie algebras. Since this goal is
shared by quite a few other books, we should explain in this Preface how our
approach differs, although the potential reader can probably see this better
by a quick browse through the book.
Representation theory is simple to define: it is the study of the ways in
which a given group may act on vector spaces. It is almost certainly unique,
however, among such clearly delineated subjects, in the breadth of its interest
to mathematicians. This is not surprising: group actions are ubiquitous in 20th
century mathematics, and where the object on which a group acts is not a
vector space, we have learned to replace it by one that is {e.g., a cohomology
group, tangent space, etc.}. As a consequence, many mathematicians other
than specialists in the field {or even those who think they might want to be}
come in contact with the subject in various ways. It is for such people that
this text is designed. To put it another way, we intend this as a book for
beginners to learn from and not as a reference. | en_US |
