Related papers: Asymptotically saturated toric algebras
This article is a survey on the cohomology of a reductive algebraic group with coefficients in twisted representations. A large part of the paper is devoted to the advances obtained by the theory of strict polynomial functors initiated by…
We study the limit of asymptotically free massive integrable models in which the algebra of nonlocal charges turns into affine algebra. The form factors of fields in that limit are described by KZ equations on level 0. We show the limit to…
The property of some finite W algebras to be the commutant of a particular subalgebra of a simple Lie algebra G is used to construct realizations of G. When G=so(4,2), unitary representations of the conformal and Poincare algebras are…
This paper surveys basic properties of finite presentation in groups, Lie algebras and rings. It includes some new results and also new, more elementary proofs, of some results that are already in the literature. In particular, we discuss…
We describe the rings of invariants for the finite orthogonal groups of plus type in odd characteristic acting on the defining representations. We also describe the invariants of the corresponding Sylow subgroups in the defining…
We give a conjectural algebraic description of the Fukaya category of a complexified hyperplane complement, using the algebras defined in arXiv:0905.1335 from the equivariant cohomology of toric varieties. We prove this conjecture for…
We parameterize the finite-dimensional irreducible representations of a class of pointed Hopf algebras over an algebraically closed field of characteristic zero by dominant characters. The Hopf algebras we are considering arise in the work…
Finite versions of W-algebras are introduced by considering (symplectic) reductions of finite dimensional simple Lie algebras. In particular a finite analogue of $W^{(2)}_3$ is introduced and studied in detail. Its unitary and non-unitary,…
A tagged arc on a surface is introduced by Fomin, Shapiro, and Thurston to study cluster theory on marked surfaces. Given a tagged arc system on a graded marked surface, we define its $\mathbb{Z}$-graded $\mathcal{A}_\infty$-category,…
We study weakly symmetric special biserial algebras of infinite representation type. We show that usually some socle deformation of such an algebra has non-periodic bounded modules. The exceptions are precisely the algebras whose Brauer…
Classical toric varieties are among the simplest objects in algebraic geometry. They arise in an elementary fashion as varieties parametrized by monomials whose exponents are a finite subset $\mathcal{A}$ of $\mathbb{Z}^n$. They may also be…
We confirm a conjecture by Lekili and Polishchuk that the geometric invariants which they construct for homologically smooth graded (not necessarily proper) gentle algebras form a complete derived invariant. Hence, we obtain a complete…
We present a rich source of Hopf algebras starting from a cofinite central extension of a Noetherian Hopf algebra and a subgroup of the algebraic group of characters of the central Hopf subalgebra. The construction is transparent from a…
We compute the ring structure of Floer cohomology groups of Lagrangian torus fibers in some toric Fano manifolds continuing the study of \cite{CO}. Related $\AI$-formulas hold for transversal choice of chains. Two different computations are…
In this paper, for a given finitely generated algebra (an algebraic structure with arbitrary operations and no predicates) A we study finitely generated limit algebras of A, approaching them via model theory and algebraic geometry. Along…
In this paper, we study the explicit geometry of threefolds, in particular, Fano varieties. We find an explicitly computable positive integer $N$, such that all but a bounded family of Fano threefolds have $N$-complements. This result has…
In this paper, we investigate algebraic and topological properties of the Riordan groups over finite fields. These groups provide a new class of topologically finitely generated profinite groups with finite width. We also introduce,…
We prove a conjecture of Shokurov which characterises toric varieties using log pairs.
In the context of commutative differential graded algebras over $\mathbb Q$, we show that an iteration of "odd spherical fibration" creates a "total space" commutative differential graded algebra with only odd degree cohomology. Then we…
A simple algebraic characterization of the Fano manifolds in the class of homogeneous toric bundles over a flag manifold $G^C/P$ is provided in terms of symplectic data.