Tootfinder

#Blakes7 Series D, Episode 09 - Sand
ORAC: We will be lovers for a little while, or maybe for a long while, who knows?
SOOLIN: I do. [Pulls key]
VILA: What a thought.
SOOLIN: Keller was right again.
AVON: Vila, try and bring Tarrant back up.

Series D, Episode 09 - Sand
SOOLIN: All right Avon, you've told us your theory. It wasn't a plague on Virn; it was the sand feeding off human energy. Does that mean we reckon Tarrant is dead?
AVON: Not necessarily. According to Orac's earlier information there's probably a woman down there. It's just possible that Tarrant was stronger and fitter than the three men in the Federation patrol, in which case he may have been kept alive, as Keller was kept alive, a…

Asymptotically rigid mapping class groups III: Presentations and isomorphisms
Anthony Genevois, Anne Lonjou, Christian Urech
https://arxiv.org/abs/2510.11336 https://

Asymptotically rigid mapping class groups III: Presentations and isomorphisms
This article is dedicated to the computation of an explicit presentation of some asymptotically rigid mapping class groups, namely the braided Higman-Thompson groups. To do so, we use the action of these groups on the spine complex, a simply connected cube complex constructed by the authors in a previous work. In particular, this allows to compute the abelianisations of these groups. With these new algebraic invariants we can handle many new cases of the isomorphism problem for asymptotically r…

Simple $B_4$ representations associated to cyclotomic Hecke algebras
Lilit Martirosyan, Hans Wenzl
https://arxiv.org/abs/2510.09928 https://arxiv.org/pdf/2…

Simple $B_4$ representations associated to cyclotomic Hecke algebras
We determine the structure of the cyclotomic Hecke algebra corresponding to the complex reflection group $G_{25}$ also when it is not semisimple, as long as the generators are diagonalizable. In particular, we classify all simple representations of the braid group $B_4$ for which the generators are diagonalizable and satisfy a cubic polynomial. This will be used in the classification of braided tensor categories of type $G_2$.

Hopf bimodules for bialgebroids
Sophie Chemla, Niels Kowalzig
https://arxiv.org/abs/2510.06417 https://arxiv.org/pdf/2510.06417

Hopf bimodules for bialgebroids
Generalising a result for Hopf algebras, we not only define the four possible types of Hopf modules in the bialgebroid setting but also yield the notion of two-sided two-cosided Hopf modules, also known as Hopf bimodules or tetramodules, in this realm. By explicitly formulating a fundamental theorem for Hopf modules via the concept of Hopf-Galois comodules, we prove that the category of Hopf bimodules can be endowed with the structure of a (pre-)braided monoidal category in two different ways, …

Bigpaw looks up at me
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