Tootfinder

A further study on averaging commutative and cocommutative infinitesimal bialgebras and special apre-perm bialgebras
Quan Zhao, Guilai Liu
https://arxiv.org/abs/2510.09208 https…

A further study on averaging commutative and cocommutative infinitesimal bialgebras and special apre-perm bialgebras
In order to generalize the fact that an averaging commutative algebra gives rise to a perm algebra to the bialgebra level, the notion of a special apre-perm algebra was introduced as a new splitting of perm algebras, and it has been shown that an averaging commutative and cocommutative infinitesimal bialgebra gives rise to a special apre-perm bialgebra. In this paper, we give a further study on averaging commutative and cocommutative infinitesimal bialgebras and special apre-perm bialgebras. A …

🇺🇦 #NowPlaying on KEXP's #MiddayShow
Blackfire:
🎵 What Do You See
#Blackfire
https://farmlife.bandcamp.com/track/blackfire-what-do-you-see-live-bonus-track

Chinese company Zinwa is reviving BlackBerry Classic with Android #Android

BlackBerry Classic is being revived with Android, and it can be yours for $400
A Chinese company is reviving the decade-old BlackBerry Classic with new hardware and installing Android on it for a modern experience.

Nächste Übernahme: Meta kauft Stimmengenerator PlayAI
PlayAI ist ein Startup für das Generieren von KI-Stimmen. Künftig gehört das Unternehmen samt Belegschaft zu Meta.
https://www.heise…

Kinners wir gehen rein, heute ist der 17. von 53 (!) Verhandlungstagen im #BlockProzess
https://www.mopo.de/hamburg/gericht/block-

OpenAI's blockbuster deals with Nvidia and AMD add a new layer to its complicated ownership structure and will dilute existing shareholders like Microsoft (George Hammond/Financial Times)

🇺🇦 #NowPlaying on KEXP's #PacificNotions
James K:
🎵 Collapse (falling forward blissfully all the time)
#JamesK
https://jameskmusic.bandcamp.com/track/collapse-falling-forward-blissfully-all-the-time

$\omega$-Lie bialgebras and $\omega$-Yang-Baxter equation
Yining Sun, Zeyu Hao, Ziyi Zhang, Liangyun Chen
https://arxiv.org/abs/2510.09630 https://arxiv.or…

$ω$-Lie bialgebras and $ω$-Yang-Baxter equation
In this paper, we introduce the definition of multiplicative $ω$-Lie bialgebra, which is equivalent to the Manin triples and matched pairs. We also study the $ω$-Yang-Baxter equation and Yang-Baxter $ω$-Lie bialgebra. The skew-symmetric solutions of the $ω$-Yang-Baxter equation can be used to construct Yang-Baxter $ω$-Lie bialgebra. We further introduce the concept of the $ω$-$\mathcal{O}$-operator, which can be constructed from a left-symmetric algebras, and based on the $ω$-$\mathcal{O…

🇺🇦 #NowPlaying on KEXP's #VarietyMix
Black Belt Eagle Scout:
🎵 My Heart Dreams
#BlackBeltEagleScout
https://blackbelteaglescout.bandcamp.com/track/my-heart-dreams
https://open.spotify.com/track/5dASBlWmGkymwerehQIC8o