Tootfinder

Idempotent & Nilpotent Operators and Matrices in Bicomplex Space
Anjali Anjali, Akhil Prakash, Amita Amita, Neeraj Kumar Tomar
https://arxiv.org/abs/2509.00784 https://

Idempotent & Nilpotent Operators and Matrices in Bicomplex Space
This paper explores idempotent and nilpotent operators in bicomplex spaces, focusing on their properties and behavior. We define idempotent and nilpotent matrices in this framework and derive related results. Several theorems are presented to establish conditions for the existence and behavior of bicomplex idempotent and nilpotent operators and bicomplex idempotent matrices.

Homological growth of nilpotent-by-abelian pro-p groups
Dessislava H. Kochloukova, Aline G. S. Pinto
https://arxiv.org/abs/2510.00421 https://arxiv.org/pdf…

Homological growth of nilpotent-by-abelian pro-p groups
We show that the torsion-free rank of $H_i(M, \mathbb{Z}_p)$ has finite upper bound for $i \leq m$, where $M$ runs through the pro-$p$ subgroups of finite index in a pro-$p$ group $G$ that is (nilpotent of class $c$)-by-abelian such that $ G/N'$ is of type $FP_{2cm}$.

Volumes of Nullhomotopies in Nilpotent Spaces
Kyle Hansen
https://arxiv.org/abs/2510.00159 https://arxiv.org/pdf/2510.00159

Volumes of Nullhomotopies in Nilpotent Spaces
The Shadowing Principle of Manin has proved a valuable tool for addressing questions of quantitative topology raised by Gromov in the late 1900s. The principle informally provides a way for bounded algebraic maps between differential graded algebras to be translated into nearby genuine maps between their geometric realizations. We extend this principle to finite towers of principal $K(G,n)$ fibrations, and in particular apply this construction to nilpotent spaces. As a specific application of t…

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Higher-order exceptional points unveiled by nilpotence and mathematical induction
Kenta Takata, Adam Mock, Masaya Notomi, Akihiko Shinya
https://arxiv.org/abs/2510.00623 https:/…

Higher-order exceptional points unveiled by nilpotence and mathematical induction
Non-Hermitian systems can have peculiar degeneracies of eigenstates called exceptional points (EPs). An EP of $n$ degenerate states is said to have order $n$, and higher-order EPs (HEPs) with $n \ge 3$ exhibit rich intrinsic features potential for applications. However, traditional eigenvalue-based searches for HEPs are facing fundamental limitations in terms of complexity and implementation. Here, we propose a design paradigm for HEPs based on a simple property for matrices termed nilpotence a…

Replaced article(s) found for math.LO. https://arxiv.org/list/math.LO/new
[1/1]:
- Mekler's Construction and Murphy's Law for 2-Nilpotent Groups
Blaise Boissonneau, Aris Papadopoulos, Pierre Touchard

Crosslisted article(s) found for math.AT. https://arxiv.org/list/math.AT/new
[1/1]:
- Volumes of Nullhomotopies in Nilpotent Spaces
Kyle Hansen
https://

On adjoint orbits in nilpotent ideals of a Borel subalgebra
Rupert W. T. Yu
https://arxiv.org/abs/2508.21647 https://arxiv.org/pdf/2508.21647

On adjoint orbits in nilpotent ideals of a Borel subalgebra
Let $\mathfrak{m}$ be a nilpotent ideal in the Borel subalgebra $\mathfrak{b}$ of a complex finite-dimensional semisimple Lie algebra, and $\mathfrak{m}^{\bullet}$ the subset of (ad-)nilpotent elements in $\mathfrak{b}$ such that $\mathfrak{m}$ is the minimal ideal containing them. This set is stable under the adjoint action of the corresponding Borel subgroup $B$. We prove that $\mathfrak{m}^{\bullet}$ contains a unique closed $B$-orbit which is the orbit of a nilpotent element whose support i…

The spectral Sullivan conjecture
Ishan Levy
https://arxiv.org/abs/2510.00262 https://arxiv.org/pdf/2510.00262

The spectral Sullivan conjecture
We show that any map from an infinite loop space to a $p$-complete nilpotent finite dimensional space factors canonically through a union of $p$-adic tori. This is proven via bootstrapping from the case of $B\mathbb{Z}/p\mathbb{Z}$, which is the key case of the Sullivan conjecture proven by Miller. The main step in our proof is to show that the subcategory of spectra generated by the reduced suspension spectrum of $B\mathbb{Z}/p\mathbb{Z}$ under colimits and extensions agrees with that of a Moo…

The type I dichotomy for two-step nilpotent locally compact groups
Pierre-Emmanuel Caprace, Max Carter
https://arxiv.org/abs/2509.26212 https://arxiv.org/p…

The type I dichotomy for two-step nilpotent locally compact groups
We address the type I dichotomy for two-step nilpotent locally compact groups. Invoking work of Baggett-Kleppner, we characterize the closed points of the unitary dual of such a group $G$ purely in terms of the group structure. An algebraic criterion characterizing when $G$ is a type I group is derived. We show that this criterion automatically holds if $G$ is a central extension of vector groups over a non-discrete locally compact field $k$ such that the commutator map is $k$-bilinear. As an a…