Lie operad
Okay kiddo, let me explain the "lie operad" to you. An operad is like a set of instructions that tells you how to do something. And the Lie operad is a set of instructions for doing something called Lie algebra.
Now, Lie algebra is like a special kind of math where you use what are called "brackets" to figure out how different objects interact with each other. It's like if you have some toys and you want to know how they fit together, you might try putting them next to each other and seeing if they click or if one can go in the other.
The Lie operad gives us the rules for how to use these brackets in Lie algebra. For example, it tells us that if we have two things and we want to figure out their bracket, we should subtract one from the other and see what's left. It also tells us that the bracket of three things is equal to the bracket of the first two with the third added on, but with some special swapping of terms.
Now, this might all sound a little confusing, but think of it like learning how to build with building blocks. You have to use certain shapes in certain ways to make sure everything fits together properly. Lie algebra is like building with really special building blocks, and the Lie operad gives us the instructions for how to use those blocks to make things fit together perfectly.
So in summary, the Lie operad is like a set of instructions that tells us how to use brackets to do Lie algebra, which is like building with really special building blocks that fit together in very specific ways.
Now, Lie algebra is like a special kind of math where you use what are called "brackets" to figure out how different objects interact with each other. It's like if you have some toys and you want to know how they fit together, you might try putting them next to each other and seeing if they click or if one can go in the other.
The Lie operad gives us the rules for how to use these brackets in Lie algebra. For example, it tells us that if we have two things and we want to figure out their bracket, we should subtract one from the other and see what's left. It also tells us that the bracket of three things is equal to the bracket of the first two with the third added on, but with some special swapping of terms.
Now, this might all sound a little confusing, but think of it like learning how to build with building blocks. You have to use certain shapes in certain ways to make sure everything fits together properly. Lie algebra is like building with really special building blocks, and the Lie operad gives us the instructions for how to use those blocks to make things fit together perfectly.
So in summary, the Lie operad is like a set of instructions that tells us how to use brackets to do Lie algebra, which is like building with really special building blocks that fit together in very specific ways.