Schur’s lemmas are some elementary but very useful results in group theory/representation theory. They can be also used in the theory of Lie algebras so we are going to review these results in this post (for completion). FIRST SCHUR’S LEMMA. … Continue reading
Representation theory is the part of Group Theory which is used in the main applications. Matrices acting on the members of a vector space are assigned to every element of a group. The connections between particle physics and representation theory … Continue reading
We are going to be more explicit and to work out some simple examples/exercises about elementary finite and infinite groups in this post. Example 1. Let us define the finite group of three elements as where , and such as … Continue reading
Other important concepts and definitions in group theory! Definition (22). Normal or invariant group. Let be a subgroup of other group G. We say that is a normal or invariant subgroup of G if the following condition holds: Proposition. Let … Continue reading
Today we are going to speak about two broad and main topics: cyclic groups and some general features of finite groups (a few additional properties and theorems). A cyclic group is, informally speaking, a group that can be generated by … Continue reading