Pseudo-reductive group
Imagine there is a special club of friends, called the "Pseudo-Reductive Group". In order to be part of this club, each friend has to satisfy some very specific rules.
First, each friend in the pseudo-reductive group must be a kind of mathematical object called a "ring". A ring is like a special box that has some numbers and symbols inside, and you can add, subtract, and multiply those numbers and symbols together.
Second, all the friends in the pseudo-reductive group must have a certain type of symmetry. Imagine you have a square piece of paper, and you fold it in half, then fold it in half again, and keep folding it in half over and over. If the paper looks the same no matter how many times you fold it, we say it has symmetry. All the friends in the pseudo-reductive group have a type of symmetry that works in a similar way to the folded piece of paper.
Third, each friend in the pseudo-reductive group must have a special way of transforming other mathematical objects. Imagine you have a toy car, and you can push it around and turn it upside down and spin its wheels. The friends in the pseudo-reductive group have a special set of rules for how to transform other mathematical objects, like the way you can transform the toy car.
So, in summary, a pseudo-reductive group is like a club of friends who are all "rings", who have a certain type of symmetry, and who have special ways of transforming other mathematical objects.
First, each friend in the pseudo-reductive group must be a kind of mathematical object called a "ring". A ring is like a special box that has some numbers and symbols inside, and you can add, subtract, and multiply those numbers and symbols together.
Second, all the friends in the pseudo-reductive group must have a certain type of symmetry. Imagine you have a square piece of paper, and you fold it in half, then fold it in half again, and keep folding it in half over and over. If the paper looks the same no matter how many times you fold it, we say it has symmetry. All the friends in the pseudo-reductive group have a type of symmetry that works in a similar way to the folded piece of paper.
Third, each friend in the pseudo-reductive group must have a special way of transforming other mathematical objects. Imagine you have a toy car, and you can push it around and turn it upside down and spin its wheels. The friends in the pseudo-reductive group have a special set of rules for how to transform other mathematical objects, like the way you can transform the toy car.
So, in summary, a pseudo-reductive group is like a club of friends who are all "rings", who have a certain type of symmetry, and who have special ways of transforming other mathematical objects.