Introduction to Representation Theory

“Introduction to Representation Theory” provides a foundational exploration of the essential concepts within the field, offering readers a clear understanding of representation theory’s key principles. This textbook delves into the intricate relationships between algebraic structures, including groups, algebras, and vector spaces, shedding light on the ways in which abstract algebraic objects can be represented through linear transformations. From finite groups to Lie groups, the book covers a spectrum of topics, including group actions, homology, and cohomology groups, providing a comprehensive introduction to this branch of mathematics.

The inclusion of keywords such as Abelian group, algebra, and Lie algebra underscores the book’s focus on various algebraic structures and their representations. With a concise yet thorough approach, this textbook is ideal for students and researchers seeking a solid foundation in the principles of representation theory and its applications across diverse mathematical domains.

Keywords

Abelian Group, Algebra, Cohomology, Cohomology Group, Finite Group, Group Action, Homology, Lie Algebra, Lie Group, Representation Theory, Vector Space