Locally compact quantum group

Okay kiddo, so a locally compact quantum group is like a special kind of group but instead of being made of regular numbers, it's made of strange things called quantum numbers.

Imagine you have a box of candies, and you want to share them equally with your friends. You can do that by dividing the candies into equal parts and giving one part to each friend.

Similarly, a group is like a box of numbers that you can divide up and give to your friends. But with quantum numbers, it's a little different.

Quantum numbers are like candies that can be in two places at the same time, because they follow some strange rules from physics. This makes sharing them around a little tricky.

So a locally compact quantum group is a special kind of group that understands these quantum rules and knows how to share them out properly. It's like a really clever friend who can divide up the candies in a way that makes everyone happy, even though they're magic candies.

But the "locally compact" part just means that this group is like a big box of candies, with some parts that are really close together and some that are far away. This is important because it helps the group understand how to share out the quantum numbers in different situations.

So that's basically what a locally compact quantum group is - a clever friend who knows how to share out magic candies properly, even when they're in different places and follow strange rules.