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# ðŸ“™ Representation Theory of Finite Groups: Algebra and Arithmetic by Steven H. Weintraub â€” pdf free

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Representation theory plays important roles in geometry, algebra, analysis, and mathematical physics. In particular, it has been one of the great tools in the study and classification of finite groups. The theory contains some particularly beautiful results: Frobenius's theorem, Burnside's theorem, Artin's theorem, Brauer's theorem--all of which are covered in this textbook. Some seem uninspiring at first but prove to be quite useful. Others are clearly deep from the outset. And when a group (finite or otherwise) acts on something else (as a set of symmetries, for example), one ends up with a natural representation of the group. ## About book:

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This book is an introduction to the representation theory of finite groups from an algebraic point of view, regarding representations as modules over the group algebra. The approach is to develop the requisite algebra in reasonable generality and then to specialize it to the case of group representations. Methods and results particular to group representations, such as characters and induced representations, are developed in depth. Arithmetic comes into play when considering the field of definition of a representation, especially for subfields of the complex numbers. The book has an extensive development of the semisimple case, where the characteristic of the field is zero or is prime to the order of the group, and builds the foundations of the modular case, where the characteristic of the field divides the order of the group.

- Series:
**Graduate Studies in Mathematics** - Author:
**Steven H. Weintraub** - Year:
**2003** - Publisher:
**Oxford University Press** - Language:
**English** - ISBN:
**0821832220,9780821832226**

- DPI:
**300** - File size:
**1 290 698** - Format:
**djvu**

Security code:

These proceedings are from the Tenth International Conference on Representations of Algebras and Related Topics (ICRA X) held at The Fields Institute. In addition to the traditional "instructional" workshop preceding the conference, there were als...

Representation Theory and Higher Algebraic K-Theory is the first book to present higher algebraic K-theory of orders and group rings as well as characterize higher algebraic K-theory as Mackey functors that lead to equivariant higher algebraic K-theory an...

The authors aim to treat the basic theory of representations of finite groups of Lie type, such as linear, unitary, orthogonal and symplectic groups. They emphasize the Curtis-Alvis duality map and Mackey's theorem and the results that can be deduced fro...

The authors aim to treat the basic theory of representations of finite groups of Lie type, such as linear, unitary, orthogonal and symplectic groups. They emphasize the Curtis-Alvis duality map and Mackey's theorem and the results that can be deduced fro...

The authors aim to treat the basic theory of representations of finite groups of Lie type, such as linear, unitary, orthogonal and symplectic groups. They emphasize the Curtis-Alvis duality map and Mackey's theorem and the results that can be deduced fro...

Introducing the representation theory of groups and finite dimensional algebras, first studying basic non-commutative ring theory, this book covers the necessary background on elementary homological algebra and representations of groups up to block theory...

This volume contains the proceedings of the Tsukuba International Conference on Representations of Algebras and Related Topics (fifth ICRA), held at the University of Tsukuba, August 13--18, 1990. The conference focused on the rapid development of ...

This book serves as a comprehensive introduction to the representation theory of Artin algebras, a branch of algebra. Written by three distinguished mathematicians, it illustrates how the theory of almost split sequences is utilized within representation ...

This is the first of two volumes providing an introduction to modern developments in the representation theory of finite groups and associative algebras, which have transformed the subject into a study of categories of modules. Thus, Dr. Benson's unique ...