Tootfinder

Complex structures on two-step nilpotent Lie groups
Maria Laura Barberis
https://arxiv.org/abs/2508.05885 https://arxiv.org/pdf/2508.05885

Complex structures on two-step nilpotent Lie groups
We give a characterization of the $2$-step nilpotent Lie algebras whose corresponding Lie groups admit a left invariant complex structure. This is done by considering separately the cases when the complex structure is 2-step or 3-step nilpotent in the sense of [Cordero-Fernández-Gray-Ugarte, 2000]. We also study the Hermitian geometry 2-step nilpotent Lie groups. We show that if a left invariant Hermitian metric on such Lie group is pluriclosed, then the corresponding complex structure is 2-st…

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.

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…

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…

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A note on multivariate diam mean equicontinuity and frequent stability
Lino Haupt, Tobias J\"ager, Chunlin Liu
https://arxiv.org/abs/2506.23313 https:…

A note on multivariate diam mean equicontinuity and frequent stability
Let $(X,G)$ be a topological dynamical system, given by the action of a is a countable discrete infinite group on a compact metric space $X$. We prove that if $(X,G)$ is minimal, then it is either diam-mean $m$-equicontinuious or diam-mean $m$-sensitive. Similarly, $(X,G)$ is either frequently $m$-stable or strongly $m$-spreading. Further, when $G$ is abelian (or, more generally, virtually nilpotent), then the following statements are equivalent: $\bullet$ $(X,G)$ is a regular $m$-to-one exte…

A Comparative Study of Delta Parquet, Iceberg, and Hudi for Automotive Data Engineering Use Cases
Dinesh Eswararaj, Ajay Babu Nellipudi, Vandana Kollati
https://arxiv.org/abs/2508.13396

A Comparative Study of Delta Parquet, Iceberg, and Hudi for Automotive Data Engineering Use Cases
The automotive industry generates vast amounts of data from sensors, telemetry, diagnostics, and real-time operations. Efficient data engineering is critical to handle challenges of latency, scalability, and consistency. Modern data lakehouse formats Delta Parquet, Apache Iceberg, and Apache Hudi offer features such as ACID transactions, schema enforcement, and real-time ingestion, combining the strengths of data lakes and warehouses to support complex use cases. This study presents a comparati…

Local limit theorems on relatively hyperbolic groups with respect to virtually nilpotent subgroups
Matthieu Dussaule
https://arxiv.org/abs/2507.15408 https…

Local limit theorems on relatively hyperbolic groups with respect to virtually nilpotent subgroups
Given a probability measure on a finitely generated group, the local limit problem consists in finding asymptotics of $p_n(e,e)$, the probability that the random walk at time $n$ is at the origin. We give the classification of all possible local limit theorems, up to bounded error, for finitely supported, symmetric, admissible probability measures on a relatively hyperbolic group with respect to virtually nilpotent subgroups.

Idefix-Closed Languages and Their Application in Contextual Grammars
Marvin K\"odding, Bianca Truthe
https://arxiv.org/abs/2507.15312 https://arxiv.or…

Idefix-Closed Languages and Their Application in Contextual Grammars
In this paper, we continue the research on the power of contextual grammars with selection languages from subfamilies of the family of regular languages. We investigate infix-, prefix-, and suffix-closed languages (referred to as idefix-closed languages) and compare such language families to some other subregular families of languages (finite, monoidal, nilpotent, combinational, (symmetric) definite, ordered, non-counting, power-separating, commutative, circular, union-free, star, and comet …