Chevalley basis
You know how when you learn math, you start with the basics like adding and subtracting and then move on to more advanced things? Well, mathematicians have a way of doing this for something called Lie algebras (which are like special kinds of mathematical objects).
The Chevalley basis is a way of breaking down a Lie algebra into smaller parts, kind of like breaking apart a toy to see how it works. Instead of just adding and subtracting, we use other special moves to get these smaller parts. And just like how we use numbers in math, these smaller parts are made up of special things called "generators" and "relations."
It might sound complicated, but by using the Chevalley basis, we can better understand Lie algebras and how they work. Imagine trying to build a puzzle without any picture or instructions - that's what it can be like to understand Lie algebras without breaking them apart using the Chevalley basis.
So, Chevalley basis helps us study Lie algebras by taking them apart, examining the smaller pieces, and seeing how they fit together to make the whole thing work.
The Chevalley basis is a way of breaking down a Lie algebra into smaller parts, kind of like breaking apart a toy to see how it works. Instead of just adding and subtracting, we use other special moves to get these smaller parts. And just like how we use numbers in math, these smaller parts are made up of special things called "generators" and "relations."
It might sound complicated, but by using the Chevalley basis, we can better understand Lie algebras and how they work. Imagine trying to build a puzzle without any picture or instructions - that's what it can be like to understand Lie algebras without breaking them apart using the Chevalley basis.
So, Chevalley basis helps us study Lie algebras by taking them apart, examining the smaller pieces, and seeing how they fit together to make the whole thing work.