A Borel subgroup is a maximal connected solvable subgroup of a linear algebraic group, often used in the study of the group's structure and representation theory. They play a crucial role in the classification of algebraic groups and the understanding of flag varieties, as they are closely related to parabolic subgroups.

Borel Subgroup

Maximal connected solvable subgroup

A linear algebraic group is a group that is also an algebraic variety, meaning it is defined by polynomial equations and the group operations of multiplication and inversion are given by regular functions. These groups play a crucial role in the study of symmetries in algebraic geometry and are instrumental in understanding the structure of solutions to polynomial equations.

Linear Algebraic Group

Group's structure

Representation Theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces. This approach allows complex algebraic problems to be translated into more manageable linear algebra problems, providing deep insights into the symmetry and structure of mathematical objects.

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