Tootfinder

On the Borel complexity of the space of left-orderings of nilpotent groups
Emir Molina Tauc\'an
https://arxiv.org/abs/2507.06953 https://

On the Borel complexity of the space of left-orderings of nilpotent groups
We give the first examples of nonabelian left-orderable groups such that the conjugacy orbit equivalence relation on its space of orders has infinity orbits, yet it is smooth in the Borel sense. The examples are all nilpotent groups and we provide a sufficient condition so that the space of orders of a nilpotent group has a smooth conjugacy orbit relation. We also show with different examples that nilpotence is not a sufficient condition for smoothness.

The geometric classification of nilpotent Lie-Yamaguti, Bol and compatible Lie algebras
Kobiljon Abdurasulov, Abror Khudoyberdiyev, Feruza Toshtemirova
https://arxiv.org/abs/2506.05353

The geometric classification of nilpotent Lie-Yamaguti, Bol and compatible Lie algebras
The geometric classifications of complex $4$-dimensional nilpotent Lie-Yamaguti algebras, $4$-dimensional nilpotent Bol algebras, and $4$-dimensional nilpotent compatible Lie algebras are given.

Classification of Equivariant Legendrian Embeddings of Rational Homogeneous Spaces into Nilpotent Orbits
Minseong Kwon
https://arxiv.org/abs/2507.03932 htt…

Classification of Equivariant Legendrian Embeddings of Rational Homogeneous Spaces into Nilpotent Orbits
For a complex semi-simple Lie algebra, every nilpotent orbit in its projectivization comes with a complex contact structure. For each nilpotent orbit, we classify projective Legendrian subvarieties that are homogeneous under the actions of their stabilizers in the adjoint group. In particular, we present a classification of equivariant Legendrian embeddings of rational homogeneous spaces into adjoint varieties.

On the rigidity of k-step nilpotent graph Lie algebras
Josefina Barrionuevo, Paulo Tirao
https://arxiv.org/abs/2507.04063 https://arx…

On the rigidity of k-step nilpotent graph Lie algebras
We thoroughly explore the class of k-step nilpotent Lie algebras associated with a simple graph looking for k-step nilpotent Lie algebras which are rigid in the variety of at most k-step nilpotent Lie algebras. We find out that, besides the complete graph, the only examples arise for k=2 and graphs of at most 4 vertices. A key tool to prove non-k-rigidity in this context, is a general construction of non-trivial deformations for naturally graded nilpotent Lie algebras.

Motives of Certain Hyperplane Sections of Milnor Hypersurfaces
Evan Marth
https://arxiv.org/abs/2507.05434 https://arxiv.org/pdf/2507…

Motives of Certain Hyperplane Sections of Milnor Hypersurfaces
We construct a hyperplane section $Y$ of a Milnor hypersurface associated to a semisimple endomorphism $φ$. Exploiting its structure as a hyperplane section of a projective bundle and its natural torus action, we give a motivic decomposition of $Y$, which encodes both the cellular structure of $Y$ and the arithmetic of the eigenvalues of $φ$. This decomposition is proven without using the "nilpotence principle", that is to say there are no "phantoms".

Gauge-invariant action for free string field theory with boundary
Carlo Maccaferri, Alberto Ruffino, Jakub Vo\v{s}mera
https://arxiv.org/abs/2506.05969 htt…

Gauge-invariant action for free string field theory with boundary
We construct fully gauge-invariant kinetic terms for open and closed string field theories on a target space with boundary. This is realized by promoting the gauge parameters at the boundary to extra dynamical modes describing boundary degrees of freedom. Having a gauge-invariant classical action, we also construct the corresponding BV master action and show that the master equation is obeyed thanks to a peculiar nilpotent structure of the BV kinetic operator. From this general construction we …

This https://arxiv.org/abs/2506.02885 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On an extension of Shlyk's theorem
In this paper, we prove that the intersection of all non-nilpotent maximal subgroups of a non-solvable group containing the normalizer of some Sylow subgroup is nilpotent, which provides an extension of Shlyk's theorem.

Invariant Hilbert spaces of distribution vectors in Lie group representations
Ingrid Beltita, Daniel Beltita
https://arxiv.org/abs/2507.05988 https://

Invariant Hilbert spaces of distribution vectors in Lie group representations
For every unitary irreducible representation of a nilpotent Lie group we prove that the representation Hilbert space is the only nonzero invariant Hilbert space of distribution vectors.

On UK left strategy.
James Schneider, Building the Party — Sidecar
https://newleftreview.org/sidecar/posts/building-the-party?pc=1693

James Schneider, Building the Party — Sidecar
An interview with James Schneider.

This https://arxiv.org/abs/2506.00952 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the class-breadth conjecture
The class-breadth conjecture of Leedham-Green, Neumann and Wiegold states that for each $p$-group, $cl(G)\leq b(G) + 1$, where $cl(G)$, $b(G)$ denote the nilpotency class and the breadth of $G$. While several counter-examples to this conjecture have been found for $p = 2$, it is still open in general for $p > 2$. This article is dedicated to one simplified version of the conjecture for $p > 2$.