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Modular Representation Theory
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Summary
Modular Representation Theory
studies the
Representation of algebraic structures
, such as groups, over a field with
Positive Characteristic
, particularly focusing on how these representations differ from those over fields of
Characteristic Zero
. This theory is essential for understanding the
Representations of finite groups
, especially in cases where the
Field's characteristic
divides the
Group's order
, leading to phenomena like indecomposable representations and the
Failure of Maschke's theorem
.
Concepts
Representation Theory
Finite Groups
Algebraic Structures
Field Characteristic
Maschke's Theorem
Indecomposable Representations
Projective Modules
Simple Modules
Blocks Of A Group Algebra
Brauer's Theorems
Green's Correspondence
Decomposition Numbers
Modular Characters
Alperin's Weight Conjecture
Defect Groups
Classification Of Finite Simple Groups
Relevant Degrees
Algebra 60%
Combinatorial Analysis and Graph Theory 20%
Number Theory 20%
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