Related papers: Twisted forms of commutative monoid structures on …
Let $X:=\mathbb{A}^{n}_{R}$ be the $n$-dimensional affine space over a discrete valuation ring $R$ with fraction field $K$. We prove that any pointed torsor $Y$ over $\mathbb{A}^{n}_{K}$ under the action of an affine finite type group…
We prove that two finite-dimensional commutative algebras over an algebraically closed field are isomorphic if and only if they give rise to isomorphic representations of the category of finite sets and surjective maps.
In this paper, for an arbitrary Kac-Moody Lie algebra $\mathfrak g$ and a diagram automorphism $\mu$ of $\mathfrak g$ satisfying certain natural linking conditions, we introduce and study a $\mu$-twisted quantum affinization algebra…
The paper is devoted to the investigation of finite dimensional commutative nilpotent (associative) algebras N over an arbitrary base field of characteristic zero. Due to the lack of a general structure theory for algebras of this type (as…
Let k be a commutative ring. We find and characterize a new family of twisted planes (i. e. associative unitary k-algebra structures on the k-module k[X,Y], having k[X] and and k[Y] as subalgebras).Similar results are obtained for the…
We study generic graded contractions of Lie algebras from the perspectives of group cohomology, affine algebraic geometry and monoidal categories. We show that generic graded contractions with a fixed support are classified by a certain…
This is a survey of recent advances in commutative algebra, especially in mixed characteristic, obtained by using the theory of perfectoid spaces. An explanation of these techniques and a short account of the author's proof of the direct…
This is a sequel to arXiv:2506.13656, in which an approach to construct a class of generalized Frobenius manifold structures on the orbit spaces of affine Weyl groups is presented. In this paper we apply this construction to the affine Weyl…
Building on structure observed in equivariant homotopy theory, we define an equivariant generalization of a symmetric monoidal category: a $G$-symmetric monoidal category. These record not only the symmetric monoidal products but also…
We construct irreducible modules for twisted toroidal Lie algebras and extended affine Lie algebras. This is done by combining the representation theory of untwisted toroidal algebras with the technique of thin coverings of modules. We…
We analyze string theory backgrounds that include different kinds of orientifold planes and map out a natural correspondence to (twisted) affine Kac-Moody algebras. The low-energy description of specific BPS states in these backgrounds…
We consider the Kronecker quiver and determine the relations for the specialisation to q=0 of the generic composition algebra as well as those for Reineke's composition monoid. We also obtain a normal form for the varieties occurring in the…
We describe affine monoids whose group of invertible elements is an active semidirect product of a unipotent group and a torus, in terms of comultiplications on the algebra of regular functions. We introduce the notion of a root monoid,…
We classify meromorphic affine connections on compact complex surfaces with algebraic dimension one, extending the work of Inoue,Kobayashi and Ochiai (1981) in the holomorphic case. The motivation is to investigate possible extension of the…
We introduce a canonical structure of a commutative associative filtered algebra with the unit on polynomial smooth valuations, and study its properties. The induced structure on the subalgebra of translation invariant smooth valuations has…
Let $W$ be a finite dimensional algebraic structure (e.g. an algebra) over a field $K$ of characteristic zero. We study forms of $W$ by using Deligne's Theory of symmetric monoidal categories. We construct a category $\mathcal{C}_W$, which…
We compute the quiver of any monoid that has a basic algebra over an algebraically closed field of characteristic zero. More generally, we reduce the computation of the quiver over a splitting field of a class of monoids that we term…
In this paper we provide a "combinatorial" description of the category of tilting perverse sheaves on the affine flag variety of a reductive algebraic group, and its free-monodromic variant, with coefficients in a field of positive…
This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic…
We study the moduli space of A/2 half-twisted gauged linear sigma models for NEF Fano toric varieties. Focusing on toric deformations of the tangent bundle, we describe the vacuum structure of many (0,2) theories, in particular identifying…