reference request – On closed connected subgroups maximum of a connected connected semi-simple Lie group?

Let $ G $ to be a semi-simple Lie group connected compact and let $ mathfrak g $ denote his Lie algebra.
Does Dynkin's classification of maximal Lie subalgebras imply the following result?

There is $ mathfrak h_1, dots, mathfrak h_r $ Lie subalgebras of $ mathfrak g $ such as: (1) for any Lie subalgebra $ mathfrak a $ of $ mathfrak g $ there is $ in G $ such as $ textrm {Ad} _a ( mathfrak a) subset mathfrak h_i $ for some people $ i $;
(2) if a Lie subalgebra $ mathfrak a $ of $ mathfrak g $ contains correctly $ mathfrak h_i $ for some people $ i $then $ mathfrak a = mathfrak g $;
(3) for each $ i $, the only connected Lie subgroup $ H_i $ of $ G $ with Lie algebra $ mathfrak h_i $ is closed $ G $.

I am satisfied that the answer is affirmative except for the number of Lie subalgebras. $ mathfrak h_i $.
I hope that there is a precise (modern) reference for this.

Some related questions:

Modern Reference for Maximum Connected Subgroups of Compact Lie Groups

Maximum subgroups of semi-simple Lie groups

Is it possible to simulate a wired Ethernet connection while connected to WiFi? Or even to detect that I am in Wifi?

I've seen a similar question here regarding the simulation of a non-internet connection to a router, when connecting to the Internet via a "network bridge". I have a slightly different problem.

I work under several home work contracts involving a wired Ethernet connection (no Wi-Fi allowed). My Wifi is pretty stable, and there should be no problem with that. Until now, in three years, I've never had an employer that "blocks me" in Wifi, so I guess they have no way to detect it.

Despite this, I am curious to know if there is a way to detect it and, if so, there is a way for me to show a wired connection while staying in Wifi.

Minor detail: For some reason, my laptop simply can not connect to my home Internet network with a wire. It never works and I do not know why. If I connect an ethernet cable to the router that my band uses for our live mixer, it connects very well (no internet), but with my home router (either the modem provided by my ISP or a separate router ), it shows a connection. That's the only reason I use Wifi, otherwise I would not even ask about it. It is also for this reason that I am afraid that the purchase of additional hardware and the use of a network bridge will fail.

graphs and networks – how to trace connected components in the community structure layout format

I have the following code plot the community structure of the random graph g. As can be seen, the community structure plot has a good visual impact. I like to generate a similar graph for connected components of g using Connected Components[g]. HighLightGraph shows individual vertices in a given component with the same color but this type of presentation is not very useful for me. I like to see components related to each other through binary links between components.

g = RandomGraph[{30, 50}, DirectedEdges -> True];
gg = Connected Components[g];
CommunityGraphPlot[g, CommunityRegionStyle -> LightGray, 
Method -> "Centrality"];
HighlightGraph[g, Subgraph[g, #] & / @ @ gg];

Thank you.

sharepoint online – Can an Office 365 group be connected to multiple site collections at the same time?

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co.combinatorics – Connected Components $ 0-1 $ matrices (rank dependence) – II

Let $ M $ be a $ 0-1 matrix.

Here, a matrix has a component means that we can browse it from a matrix input $ (i, j) $ Which one is $ 1 $ to any other by moving the stage of $ (i pm1, j), (i, j pm1), (i pm1, j pm1) $ where every step you make you walk on another $ 1 $.

Each row $ 1 $ matrix with $ 0 / $ 1 the entries can be converted to a matrix of a component by permutating rows and columns.

On the other hand at each $ n $ there are matrices that can not be brought to a rank.

Is there a lower limit on

  1. $ mathbb R $ rank $ r $

  2. $ mathbb F_2 $ rank $ r $

as a function of $ n $ beyond which all $ 0 / $ 1 size matrices $ n times n $ can not be brought to a component?

Which matrix classes can not have a component?

Can I use the phone's microphone when connected to a Bluetooth speaker?

When you connect the phone to a BT speaker with a microphone (almost all of them), the speaker behaves like a BT headset and the phone's microphone is turned off.

Can I use the speaker for audio output only, using the phone's internal microphone?

interaction design – Ask users to connect while they are already connected

For me, this UI element reminds the user that he or she has a relationship with the website in question, even if the user is currently disconnected from the site.

For example, I have used various travel booking sites and, for some, I could have an account, and with others, I may have done a transaction as well. 39; "guest". Plus, booking trips is something I rarely do, so it's hard to remember if I have an account on a particular website. So, if (for example) Expedia greets me with a "Hello Mark!" S & # 39; identify", my name inexorably draws my attention to this element of the UI and tells me that I have an account, and therefore a registered credit card, a transaction history, loyalty points, and so on.

Basically, this template reminds the user of their relationship with the service and allows them to sign in to reconnect to the site. From the point of view of the online service view, this may cause the user to interact more meaningfully with the site (i.e., in a connected state).

what is connected (00000005) and check the return: 1 in the command openssl s_client

I'm trying to test the icinga2 client and server connectivity with the openssl command and I'm using a command such as the following line in the client

openssl s_client -CAfile /var/lib/icinga2/certs/ca.crt-cert / var / lib / icinga2 / certs /.crt -key /var/lib/icinga2/client.key -connect

and I get an exit like

CONNECTED (00000005)
depth = 1 CN = Icinga CA
check the return: 1
depth = 0 CN =
check the return: 1

My question is, what is CONNECTED (00000005) and check the return: 1 means ?

It must be CONNECTED (00000003) according to the icinga2 documentation. I do not know what is the difference between CONNECTED (00000005) and CONNECTED (00000003)

Thank you

representation theory – Quiver algebras simply connected

Let $ A $ to be an algebra of quiver representation-finite. In that case $ A $ is simply connected if and only if his first cohomology of Hochschild disappears under the effect of Buchweitz and Liu. $ A $ is called strongly simply connected in case each convex subcategory of $ A $ is simply connected.

The importance of this notion is for example shown in the following result of Bongartz which gives a strong generalization of Gabriel's theorem:

Theorem: In case $ A $ is a finite representation and very simply connected, there is a bijection between the indecomposable $ A $-modules and all of the positive roots of the Tits form of $ A $ (sending a dimension vector to a root).

Question 1: Is there a simple example showing that the theorem is wrong when we replace "strongly connected simply" with "simply connected"?

Question 2: Is there a test (fast) with the computer (using QPA) to check if a given representation-finite algebra is strongly connected? The direct way would probably be to check if $ HH ^ 1 (eAe) = $ 0 for any basic idempotent $ e $, which is possible but takes too much time with the computer for most algebras.

Question 3: In case $ A $ is a representation-finite quiver algebra of finite global dimension such that $ mathrm {Ext} _A ^ 1 (M, M) = 0 $ for any indecomposable $ A $-module $ M $ and such that each radical of an indecomposable projective module is indecomposable (this implies that $ A $ has the separation condition), is it true that $ A $ is strongly connected?

Cancel key function on a Bluetooth device connected to an Android phone

Double-click the play / pause button Bluetooth Headset Tagg inferno calls the last number dialed. How can I replace it to ignore the currently playing track

Anyone facing this problem. I would love any suggestion of application that would help me overcome this problem.