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Preprint Sep 2026

Topological Band Theory for High-Dimensional Parameter Spaces

We study the topological band theory of quantum Hall systems in which the adiabatic flux parameters of an external gauge potential form a high-dimensional manifold. This situation arises both for strongly correlated matter on spatial Riemann surfaces of genus $g>1$, as well as in the formal study of matter on compact o...

Vivek Chakrabhavi, W. Chavarria, J. Heckman et al. · 0 citations
Preprint Sep 2026

Homological properties of quantum groups governed by small quantum groups

We develop a general characteristic-free framework for studying the homological properties of a broad class of module-finite Hopf algebras. This framework makes it possible to reduce the study of the homological properties of many quantum groups at roots of unity and their multiparameter deformations to the study of th...

Yi-Min Huang, Tian-Cheng Qi, Quan-Shui Wu et al. · 0 citations
Preprint Aug 2026

Quantum regularity of finite dimensional semisimple algebras

In this paper, we establish a necessary and sufficient criterion for a finite-dimensional semisimple algebra over an algebraically closed field of characteristic $0$ to admit a regular quantum commutative decomposition. We apply this characterization to group algebras and show that a finite group algebra admits such a...

Y. Bahturin, L. Centrone, Kauê Pereira · 0 citations
Preprint Sep 2026

Refining invariants of finite groups with class functions

Many numerical invariants of a finite group arise as the multiplicity of the trivial character in a naturally associated class function, and the remaining multiplicities carry finer structural information. For the number of conjugacy classes of elements whose order involves only a chosen set of primes, the natural such...

Christopher A. Schroeder · 0 citations
Preprint Sep 2026

Automorphism Groups of Three-Dimensional Leibniz Algebras: A Complete Description

Automorphism groups are among the most natural structural invariants of an algebra, and their explicit determination is a basic problem in the structure theory of Leibniz algebras. In a series of earlier papers, automorphism groups were obtained for several classes of low-dimensional, one-generated, nilpotent, and non-...

L. Kurdachenko, O. Pypka, M. Semko · 0 citations
Preprint Sep 2026

Stringy invariants for abelian character varieties

We compute all stringy invariants, encoding orbifold cohomology numbers, of (the normalization of) the identity component of $G$-character varieties of free abelian groups and of moduli spaces of $G$-Higgs bundles on abelian varieties, for all complex connected reductive groups $G$. As an application, we provide a dire...

C. Florentino, Ángel González-Prieto, Alfonso Zamora · 0 citations

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