пишут что иногда в ряд R,C,H,O,... между кватернионами H и октонионами O уместно добавить шестимерную алгебру секстонионов S (определение на картинке; U=R^2).
Например, можно определить проективную плоскость SP^2 — 12-мерное вещественное алгебраическое многообразие. Особые точки образуют RP^5, их дополнение — векторное расслоение ранга 4 над Gr(2,R^6). (а проективная прямая SP^1 — особая квадрика в RP^7)
А ещё так можно построить (не простую) алгебру Ли e_{7.5}, которая сидит между (исключительными простыми) алгебрами Ли e_7 и e_8 https://arxiv.org/abs/math/0402157
пишут что иногда в ряд R,C,H,O,... между кватернионами H и октонионами O уместно добавить шестимерную алгебру секстонионов S (определение на картинке; U=R^2).
Например, можно определить проективную плоскость SP^2 — 12-мерное вещественное алгебраическое многообразие. Особые точки образуют RP^5, их дополнение — векторное расслоение ранга 4 над Gr(2,R^6). (а проективная прямая SP^1 — особая квадрика в RP^7)
А ещё так можно построить (не простую) алгебру Ли e_{7.5}, которая сидит между (исключительными простыми) алгебрами Ли e_7 и e_8 https://arxiv.org/abs/math/0402157
Telegram has become more interventionist over time, and has steadily increased its efforts to shut down these accounts. But this has also meant that the company has also engaged with lawmakers more generally, although it maintains that it doesn’t do so willingly. For instance, in September 2021, Telegram reportedly blocked a chat bot in support of (Putin critic) Alexei Navalny during Russia’s most recent parliamentary elections. Pavel Durov was quoted at the time saying that the company was obliged to follow a “legitimate” law of the land. He added that as Apple and Google both follow the law, to violate it would give both platforms a reason to boot the messenger from its stores. Meanwhile, a completely redesigned attachment menu appears when sending multiple photos or vides. Users can tap "X selected" (X being the number of items) at the top of the panel to preview how the album will look in the chat when it's sent, as well as rearrange or remove selected media. This ability to mix the public and the private, as well as the ability to use bots to engage with users has proved to be problematic. In early 2021, a database selling phone numbers pulled from Facebook was selling numbers for $20 per lookup. Similarly, security researchers found a network of deepfake bots on the platform that were generating images of people submitted by users to create non-consensual imagery, some of which involved children. Telegram does offer end-to-end encrypted communications through Secret Chats, but this is not the default setting. Standard conversations use the MTProto method, enabling server-client encryption but with them stored on the server for ease-of-access. This makes using Telegram across multiple devices simple, but also means that the regular Telegram chats you’re having with folks are not as secure as you may believe. Some people used the platform to organize ahead of the storming of the U.S. Capitol in January 2021, and last month Senator Mark Warner sent a letter to Durov urging him to curb Russian information operations on Telegram.
from in
