Algebre Borroméene, Grothendieck's Récoltes et Semailles (contd.)

0:00 The classic class ofbert. All right, here it is 49 elements. And this is designed in the first series, with the relations that are many here, a lot of relations and some könnten angular point against this. So you can see that the representation is equal to 1, the identity, rs is equal to 1, sr is equal to 1, sr is equal to 1. And then, as there is an operation of SUP, this is the identification of the matrices, and I also have a SUP on the matrices, so r is equal to 1. You know that Boroméen is the union étroite. For the moment, it seems to be a bit more metaphorical compared to the design of Boroméen, to say that it's Boroméen. It's less if we say that it's Boroméen as a group, with the definition that I gave earlier of Boroméen in this category. But it's not possible, because for Boroméen it would be true that the Ecosian is already defined, so it's not a group, it's an endo. This will not be worth, for all that such things that we live ! So it is not Bphoméen , also the best category in which we live in the first category So if we want to have something for Bphoméen We cannot forget about which category it is left Comparison I'm not going into the future Because it is everything Termine Ah, it's cyclical, you actually see… If you destroy If you are in place in the other part, all these relations will disappear. So there will be no relation. These are the two aspects. The technical problem is not the most interesting. Now there is a new one with the real anneau of the matrices of 2S coefficients, which is in Z over 2S. So if I place now in M2, the Z equals R, the F2, it's right. Then I take the generator R, M0, 1, 1, 0. And here it is, it's really the end of the matrix. S equals 1, 0, 1, 1. And I equals 1, 1, 0, 1.

2:30 R2 is equal to 2 is equal to 1. RAS is not the same. And now it is R plus S plus Y is equal to 1. Here we have two examples quite simple. One more amusing example of the 3-symmetric, so primitaires, is the core with an element, the core with a unit. So if I take it under the form If you look at the racines of X3 plus X1, compared to X2, these three racines are called RSI and I have a relationship between the racines and the racines and the racines of X3 plus X1. All this can seem to be a bit wrong. In fact, you can ask if it is only the 3-6-8, or if, in a certain way, quitte à faire vivre l'objet dans une autre catégorie, ça peut vraiment avoir cette progrès supplémentaire du fait que quand j'ai eu un tout est fait. The next example the most interesting on which I have worked on the final level, c'est le core GL3-2. in the past, it was imposed on the mobile logic. The fact that we can find in the ensemble at 2 puissance elements 3 structures, if it is R, in the ensemble at 2 puissance elements, three structures boolean three structures boolean three structures boolean qui jouent des rôles symétriques entre elles et qui ont la propriété que les opérations de ces trois structures quand elles se mélangent avec ça je vous déclare toutes les fonctions

5:00 sur l'ensemble de la logistique en particulier dans les opérations qui n'ont fait un corps donc la multiplication du corps can be found from the logics in order to consider three families of logics. So, of a certain way, I had to consider that these three structures logics were like the three rounds, it's a neurone, it's a mix, it's a mix, to make... There's still a lot of precision to make, to describe the three structures logics, that they are in there, it depends on what they can do, You can see, each ronde, each sculpture is not null, there are relations with the W, but in the same time, it's important, by the way. So you can't find it with the one, only one, that's all. So, in the analysis of these things, I was placed by GL3-2F2. GL3-2F2 is an important group, which is the group 5, with 160 elements, that is probably considered for the first time, and we have a lot of presentations, but I gave you a presentation of Cycli, a presentation of Werner, which is not in nature, so this group GL322 has the same presentation in terms of the matrix, the first matrix is this. There are other presentations that are that I have given. I have given this one, one, one, one, one, zero, one, zero, one, one, That's R. Then S is 1, 0, 1, 1, 1, 1, and then 1, 1, 0. And I is 0, 1, 1, 1, 1, 1, 0, 1, 1, 1. I will not explain why this is the object that I said earlier, but in the case, what is true, is that the group GF3-2F2 is engendered by these three generators in a way cyclical.

7:30 Each one is in a number of 7. The idea is to find that this group is a group borromean, because it is fabricated by three generators, which are liable by the relationship between the donor and the group. The same thing that the group of the borromean, But, you know, this is the end of the day. So, you know, this is what I said earlier. So, how to do it for that it is really a problem? Well, you need to change the category. You don't want to consider it as a group. You need to consider it as a structure more, with exactly what you want to do. Since the definition vows, the definition that I gave you from the beginning, It's in the middle of the technology, I don't know how to do it. Now, look at what happens if I take this GL3, the F2, which is at the center, which is a B, and the quotient by R is equal to 1. When I look at the relations, I haven't written it here. Suppose that when I quotient by R is equal to 1, there will be relations. Of course, there will be one because the group is finished. There are relations. But these relations, there are no relations communes. There are no relations. There are no relations. For example, it's R7, R7, R7, R7, R1, R7, R1. That, that will remain. But if there is only that, then you will be able to be free and you will be free among the groups in which the elements are in process. It's because in a group where all the elements are in process. It's not an axiom equational that we can put for all the elements of a group. But it's still the idea of what we want to do. So if I add the X7 equals 1 to the X, the X7 equals 1 to the X7 equals 1, it is not necessarily equal to the X. So what I want to say is that there are relations in the quotient

10:00 and we ask if the relations which remains, they can be divided between the R and the C-C-C, between the C-G-I-A-R, so it's rather I. If there is something on the I, the R is more than I. There is something on the I on the S, and if I can put the relationship only on the I on the I on the S, then I can put the relationship that I can put, but this time it's a relationship with R, and I can add to the theory. If I can add the theory, that allows the quotient to be free in the theory of the equation. In our case, it is rather a look at the difference between the relations which will disappear or which will not disappear in the quotient. The last reason for which GL3-2 seems to be a model of the same So, that remains for the moment. It's still a bit metaphorical. The affirmation GEL32F2 and BOROMIEN, it doesn't correspond to the definition that I have given. There is no paper for the proof of the BOROMIEN. It would have to be an agency, an emergency, but it's still tentative to say that GEL32F2, it's still the smallest group of spaces. The smallest group of spaces is F2, the smallest group of spaces in BOROMIEN, I'm going to start with you. If now it's good, if it's a good manner of doing it, I don't know what to do. I don't know what to do. I'm going to pass a little bit of time. I don't want to know that it's a big difference. I'm going to stay there with the definitions, which is not a big difference. But relatively few examples... Don't relatively few examples that serve in the definition, if I get confused. Well, I get confused about all of them. Yes, of course. And the other examples... I would rather have an example. Yes, it's that. Yes, it's an example. But it's an equation for the relationship. Here, for example, when I play, there are some examples of things primitaires. There are some examples of things primitaires. In all these examples, when I kill a degenerate,

12:30 I try to kill a degenerate and I try to separate them. And if now, if I take the derivative of the enemy, and if I kill a degenerate, which is the subject, which is the module of the same. It is possible to consider that the Covid has an obstruction, the defy boronanity, of the system sanitaire that I have. The idea is that we have not only some systems that are purely boronians, but if they are not there, there is a way to calculate why they are not. in part of the system that is already active in the term. It's not a system that we can talk about, it's not a system that we can talk about.