#TITLE_ALTERNATIVE#

• Main Author: PRAKASA (NIM 10107065); Pembimbing : Dr. Muchtadi Intan Detiena, YOHENRY
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/14557
• Institution: Institut Teknologi Bandung

Algebraic Structure is introduced as the study of structures of mathematical system <br /> <br /> <br /> <br /> <br /> such as vector space, groups and rings. These structure come as the generalization <br /> <br /> <br /> <br /> <br /> of things we already know, for example, sets of real numbers R and complex numbers <br /> <br /> <br /> <br /> <br /> C, together with addition and multiplication form a field. Beside that, there are <br /> <br /> <br /> <br /> <br /> another structures called group algebras and modules. Same as an algebra over field, <br /> <br /> <br /> <br /> <br /> a group algebra has two structure: the structure of vector space and ring. Modules <br /> <br /> <br /> <br /> <br /> which we will discuss in here are modules over group algebras. Some topics that <br /> <br /> <br /> <br /> <br /> involve groups and modules over group algebras are Group Representations Theory <br /> <br /> <br /> <br /> <br /> and Character Theory. Representation theory gives us a way of visualizing a group <br /> <br /> <br /> <br /> <br /> as a group of invertible matrices. There is a close connection between CG-modules <br /> <br /> <br /> <br /> <br /> and representations. In this work, we will see how to use Character Theory to decompose <br /> <br /> <br /> <br /> <br /> a given CG-module into a direct sums of its irreducible CG-submodules. <br /> <br /> <br /> <br /> <br /> Therefore Character Theory help us to get a better understanding of CG-modules <br /> <br /> <br /> <br /> <br /> so we can easily learn Group Representation Theory.