相关论文: Finite presentation is a Morita invariant property

Consider a finite-dimensional algebra $A$ and any of its moduli spaces $\mathcal{M}(A,\mathbf{d})^{ss}_{\theta}$ of representations. We prove a decomposition theorem which relates any irreducible component of…

An algorithm for computing power conjugate presentations for finite soluble quotients of predetermined structure of finitely presented groups is described. Practical aspects of an implementation are discussed.

This is a survey on the finite basis problem for varieties of algebraic systems. Our exposition is in two directions: (i) We give numerous examples of varieties which are not finitely based. (ii) We give examples of important varieties with…

We consider affine representable algebras, that is, finitely generated algebras over a field that can be embedded into some matrix algebra over a commutative algebra. We show that this algebra can in fact be chosen to be a polynomial…

We prove a formality theorem for algebraic objects internal to smooth complex varieties that are not compact but whose mixed Hodge structure has a certain purity property.

The notion of silting mutation was introduced by Iyama and the author. In this paper we mainly study silting mutation for self-injective algebras and prove that any representation-finite symmetric algebra is tilting-connected. Moreover we…

We show that, for each finite algebra A, either it has symmetric term operations of all arities or else some finite algebra in the variety generated by A has two automorphisms without a common fixed point. We also show this two-automorphism…

Let $p$ be a prime number, and let $k$ be an algebraically closed field of characteristic $p$. We show that the tame fundamental group of a smooth affine curve over $k$ is a projective profinite group. We prove that the fundamental group of…

The main aim of the present paper is to represent an exact and simple proof for FLT by using properties of the algebra identities and linear algebra.

Keller proved in 1999 that the Gerstenhaber algebra structure on the Hochschild cohomology of an algebra is an invariant of the derived category. In this paper, we adapt his approach to show that the Gerstenhaber algebra structure on the…

Several results on presenting an affine algebraic group variety as a product of algebraic varieties are obtained.

We introduce Morita equivalence for Nijenhuis groupoids and for their infinitesimal counterparts, establishing a global-to-infinitesimal correspondence under the Lie functor. A special case is that of holomorphic Lie groupoids and…

A finitely generated commutative monoid is uniquely presented if it has only a minimal presentation. We give necessary and sufficient conditions for finitely generated, combinatorially finite, cancellative, commutative monoids to be…

We show that the Auslander-Reiten Formula for a finite dimensional hereditary algebra is invariant under the Auslander-Reiten translate.

We present a conjecture on the irreducibility of the tensor products of fundamental representations of quantized affine algebras. This conjecture implies in particular that the irreducibility of the tensor products of fundamental…

We give a complete classification of all $d$-representation-finite symmetric Nakayama algebras and of all $d$-representation-finite trivial extensions of path algebras of quivers, over an arbitrary field. As a consequence we get a…

The decision problem of membership in the Representation Class of Relation Algebras (RRA) for finite structures is undecidable. However, this does not hold for many Relation Algebra reduct languages. Two well known properties that are…

We investigate the algebras of invariants and the properties of the quotient morphism by an action of a finite group scheme in terms of stabilizers of points.

We give a necessary and sufficient smoothness condition for the scheme parameterizing the n-dimensional representations of a finitely generated associative algebra over an algebraically closed field of characteristic zero. In particular,…

In this article we study certain notions of `tameness' for the persistence modules studied in topological data analysis. In particular, we show that after adding infinitary points the so called finitely determined modules become finitely…