# Generators of R4: Find Here

• kaksmet
In summary, there was a miscommunication between the two parties in regards to the meaning of "generators of the group" and one party was looking for a basis for the 6-dimensional Lie algebra instead.

#### kaksmet

Hey

Does anyone know where I can find the generators of the group of rotations in four dimensions?

thanks!

The group of all rotation of R^4? That has an uncountable set of generators - I don't think you want to find those.

only needed a set of six that did generate the entire group. Found them, rotations "around planes" instead of around axes. thanks anyway.

matt grime said:
The group of all rotation of R^4? That has an uncountable set of generators - I don't think you want to find those.

This is an example of miscommunication between pure mathematicians and theoretical physicists, for whom the term "generators of the group" means quite different things.

Here, I think kaksmet was looking for a basis for the 6-dimensional Lie algebra of the Lie group of rotations on R^4.

## What is the purpose of generators of R4?

The purpose of generators of R4 is to provide a systematic way to generate elements of a group or algebraic structure, such as a ring or field. This allows for efficient computation of elements and their properties.

## How do generators of R4 work?

Generators of R4 work by using a set of elements to generate all other elements in a group or algebraic structure. This is done through a process of combining and multiplying the generators in different ways to create new elements.

## Why are generators of R4 important in mathematics?

Generators of R4 are important in mathematics because they provide a way to represent and manipulate abstract algebraic structures, which have many applications in various branches of mathematics and science. They also allow for efficient computation and analysis of these structures.

## What is the difference between a generator of R4 and an element of R4?

A generator of R4 is an element that, when combined with other generators, can generate all elements in a structure. An element of R4 is simply an element that belongs to the structure. Not all elements are generators, but all generators are elements.

## Can generators of R4 be used in other contexts besides algebraic structures?

Yes, generators of R4 can be used in other contexts besides algebraic structures. They can be applied to various discrete structures, such as graphs and codes, to generate all possible configurations. They can also be used in computer science and engineering to generate data sets or test cases.