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The flat semirings with nilpotent multiplicative reducts
Zidong Gao, Miaomiao Ren
https://arxiv.org/abs/2506.23047 https://arxiv.org/…

The flat semirings with nilpotent multiplicative reducts
In this paper, we focus on the variety $\mathbf{NF}_3$ generated by all flat semirings with $3$-nilpotent multiplicative reducts. By introducing graph semirings, we characterize all subdirectly irreducible members of $\mathbf{NF}_3$. We prove that the variety $\mathbf{NF}_3$ has uncountably many subvarieties and show that every finitely generated subvariety of $\mathbf{NF}_3$ is a Cross variety. Moreover, we demonstrate that $\mathbf{NF}_3$ has a unique limit subvariety, which is generated by a…

Truncated symbols of differential symmetry breaking operators
Toshihisa Kubo, V\'ictor P\'erez-Vald\'es
https://arxiv.org/abs/2506.23599 https:…

Truncated symbols of differential symmetry breaking operators
In this paper, we introduce the truncated symbol $\mathrm{symb}_0(\mathbb{D})$ of a differential symmetry breaking operator $\mathbb{D}$ between parabolically induced representations, which generalizes the symbol $\mathrm{symb}(\mathbb{D})$ for abelian nilpotent radicals to the non-abelian case. The inverse $\mathrm{symb}_0^{-1}$ of the truncated symbol map $\mathrm{symb}_0$ enables one to perform a recipe of the F-method for any nilpotent radical. As an application, we classify and construct…

Almost abelian pseudo-K\"ahler Lie algebras
Diego Conti, Alejandro Gil-Garc\'ia
https://arxiv.org/abs/2506.22278 https://arx…

Almost abelian pseudo-Kähler Lie algebras
We study invariant pseudo-Kähler structures on a solvmanifold $G$ such that the Lie algebra $\mathfrak{g}$ is almost abelian, that is $\mathfrak{g}=\mathfrak{h}\rtimes\mathbb{R}$, with $\mathfrak{h}$ abelian; comparing with the positive-definite case, an additional situation occurs, corresponding to the ideal $\mathfrak{h}$ being degenerate. We obtain a classification up to unitary isomorphism in all dimensions. We deduce that every nilpotent almost abelian Lie algebra endowed with a complex s…

The Trump administration rescinds VOA layoff notices due to document errors that could have delayed or nullified the layoffs, plans to attempt the layoffs again (Minho Kim/New York Times)
https://www.nytimes.com/2025/06/27/us/politics/trump-voa-layoffs…

Trump Administration Rescinds Voice of America Layoffs After Errors in Notices
The errors in the layoff notices could have derailed President Trump’s effort to dismantle the news organization. The administration said it would attempt the layoffs again.

The nilpotent graph of a finite0-dimensional Lie algebra
David Towers, Ismael Gutierrez, Luis Fernandez
https://arxiv.org/abs/2506.19758 https://

The nilpotent graph of a finite0-dimensional Lie algebra
Let $L$ be a finite-dimensional Lie algebra over a field $F$. In This paper we introduce the \emph{nilpotent graph} $Γ_\mathfrak{N}(L)$ as the graph whose vertices are the elements of $L \setminus \nil(L)$, where \[\nil(L) = \{x \in L \mid \langle x, y \rangle \text{ is nilpotent for all } y \in L\},\] and where two vertices $x, y$ are adjacent if the Lie subalgebra they generate is nilpotent. We give some characterizations of $\nil(L)$ and its connection with the hypercenter $Z^*(L)$, for exa…

Representation theory of hereditary artin algebras of finite representation type
Shiping Liu, Gordana Todorov
https://arxiv.org/abs/2506.22987 https://

Representation theory of hereditary artin algebras of finite representation type
Let $H$ be a hereditary artin algebra of finite representation type. We first determine all hammocks in the Auslander-Reiten quiver $\GaH$ of $\mmod H$, the category of finitely generated left $H$-modules. This enables us to obtain an effective method to construct $\GaH$ by simply viewing the ext-quiver of $H$. As easy applications, we compute the numbers of non-isomorphic indecomposable objects in $\mmod H$ and the associated cluster category $\mathscr{C}_H$, as well as the nilpotencies of the…

#Iran:
"Their solidarity with oppositional forces has been fragmentary and opportunist, devoid of any consistent anti-imperialist strategy, except in their lonely but crucial capacity as a defender of Palestinian rights, in a region where every single Arab government has capitulated to the hegemon."
Tariq Ali, Nuclear Options — Sidecar

Tariq Ali, Nuclear Options — Sidecar
Regime change in Tehran?

An Application of Maximality to Nilpotent and Finitely Generated L-Subgroups of an L-Group
Iffat Jahan, Ananya Manas
https://arxiv.org/abs/2506.20192 https…

An Application of Maximality to Nilpotent and Finitely Generated L-Subgroups of an L-Group
This paper is a continuation of the study on maximal and Frattini L-subgroups of an L-group. The normality of the maximal L-subgroups of a nilpotent L-group is explored. Then, the concept of finitely generated L-subgroup is introduced and its relation with maximal condition on L-subgroups is established. Thereafter, several results pertaining to the notions of Frattini L-subgroup and finitely generated L-subgroups have been investigated.

"Also back in style is the tactic of using disinformation to manufacture consent for war, as with Netanyahu’s claims that Iran was right on the cusp of acquiring a nuclear weapon and intending to supply one to Yemen’s Ansarallah. We are entering territory so fantastical that the ‘dodgy dossier’ and ‘45-minute WMD’ seem almost quaint by comparison."
Eskandar Sadeghi-Boroujerdi, Culmination — Sidecar

Eskandar Sadeghi-Boroujerdi, Culmination — Sidecar
Israel attacks Iran.

This https://arxiv.org/abs/2503.05572 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Word problems and embedding-obstructions in cellular automata groups on groups
We study groups of reversible cellular automata, or CA groups, on groups. More generally, we consider automorphism groups of subshifts of finite type on groups. It is known that word problems of CA groups on virtually nilpotent groups are in co-NP, and can be co-NP-hard. We show that under the Gap Conjecture of Grigorchuk, their word problems are PSPACE-hard on all other groups. On free and surface groups, we show that they are indeed always in PSPACE. On a group with co-NEXPTIME word problem, …