Related papers: The classification problem for operator algebraic …

In this article, we explore the problem of determining isomorphisms between the twisted complex group algebras of finite $p$-groups. This problem bears similarity to the classical group algebra isomorphism problem and has been recently…

The problem of classifying all short multiplets of superconformal algebras still seems to be an open question. A generic short multiplet is non-unitary, which nevertheless is of interest in various contexts. Even if one is interested in…

We classify the orbit closures in the variety Nov_3 of complex, 3-dimensional Novikov algebras and obtain the Hasse diagrams for the closure ordering of the orbits. We provide invariants which are easy to compute and which enable us to…

We consider a couple of versions of classical Kurosh problem (whether there is an infinite-dimensional algebraic algebra?) for varieties of linear multioperator algebras over a field. We show that, given an arbitrary signature, there is a…

This paper studies the restriction multiplicities of half-diagram modules for the partition algebra and their geometric interpretations. By specializing the Bowman-De Visscher-Orellana formula [BVC, Theorem 4.3] for restriction…

Polynomial factorization is a fundamental problem in computational algebra. Over the past half century, a variety of algorithmic techniques have been developed to tackle different variants of this problem. In parallel, algebraic complexity…

The present paper is devoted to an algebraic treatment of the joint spectral theory within the framework of Noetherian modules over an algebra finite extension of an algebraically closed field. We prove the spectral mapping theorem and…

The classification, both up to isomorphism or up to equivalence, of the gradings on a finite dimensional nonassociative algebra A over an algebraically closed field F, such that its group scheme of automorphisms is smooth, is shown to be…

This paper investigates the homology of the Brauer algebras, interpreted as appropriate Tor-groups, and shows that it is closely related to the homology of the symmetric group. Our main results show that when the defining parameter of the…

In recent years, much work has been done to measure and compare the complexity of orbit equivalence relations, especially for certain classes of Polish groups. We start by introducing some language to organize this previous work, namely the…

Let $R$ be a standard graded Noetherian algebra over an Artinian local ring. Motivated by the work of Achilles and Manaresi in intersection theory, we first express the multiplicity of $R$ by means of local $j$-multiplicities of various…

We classify irreducible finite-dimensional modules of a collection of real Lie superalgebras that includes the simple ones, their classical variants, complex Lie superalgebras after restriction of scalars, and all real Lie algebras. Our…

Ian Grojnowski has developed a purely algebraic way to connect the representation theory of affine Hecke algebras at an (l+1)-th root of unity to the highest weight theory of the affine Kac-Moody algebra of type A_l^(1). The present article…

In [I. Arzhantsev and M. Zaidenberg, Borel subgroups of the automorphism groups of affine toric surfaces, arXiv:2507.09679 (2025)] we described the Borel subgroups and maximal solvable subgroups of the automorphism groups of affine toric…

We show that the smooth theta divisors of general principally polarised abelian varieties can be chosen as irreducible algebraic representatives of the coefficients of the Chern-Dold character in complex cobordisms and describe the action…

We ask whether the only multiplicities in the spectrum of the clamped round plate are trivial, i.e., whether all existing multiplicities are due to the isometries of the sphere, or, equivalently, whether any eigenfunction is separated. We…

The incompressibility method is a counting argument in the framework of algorithmic complexity that permits discovering properties that are satisfied by most objects of a class. This paper gives a preliminary insight into Kolmogorov's…

We study the complexity of the classification problem of conjugacy on dynamical systems on some compact metrizable spaces. Especially we prove that the conjugacy equivalence relation of interval dynamical systems is Borel bireducible to…

The purpose of this paper is to study algebras of singular integral operators on $\mathbb{R}^{n}$ and nilpotent Lie groups that arise when one considers the composition of Calder\'on-Zygmund operators with different homogeneities, such as…

Two decades ago P. Martin and D. Woodcock made a surprising and prophetic link between statistical mechanics and representation theory. They observed that the decomposition numbers of the blob algebra (that appeared in the context of…