Abstract
After studying the J-semisimplicity problem for the group ring in the last chapter, a natural topic to discuss next will be the representation theory of groups. We have already explained, in the introduction to §6, how ring theory may be brought to bear on group representation theory by viewing representations as modules over group rings. From this viewpoint, many facts in the representation theory and character theory of finite groups can be deduced from facts concerning modules over finite-dimensional algebras. This ring-theoretic approach to group representation theory was first effectively used by Emmy Noether, and subsequently greatly popularized by her disciples and followers.
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© 2001 Springer Science+Business Media New York
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Lam, T.Y. (2001). Introduction to Representation Theory. In: A First Course in Noncommutative Rings. Graduate Texts in Mathematics, vol 131. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8616-0_3
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DOI: https://doi.org/10.1007/978-1-4419-8616-0_3
Publisher Name: Springer, New York, NY
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