Related papers: Prospecies of algebras I: Basic properties

Let $\phi\colon A\rightarrow B$ be an algebra extension. We prove that if $\phi$ is split, the derived-discreteness of $A$ implies the derived-discreteness of $B$; if $\phi$ is separable and the right $A$-module $B$ is projective, the…

We introduce a category of cluster algebras with fixed initial seeds. This category has countable coproducts, which can be constructed combinatorially, but no products. We characterise isomorphisms and monomorphisms in this category and…

This the first of a series of articles dealing with abstract classification theory. The apparatus to assign systems of cardinal invariants to models of a first order theory (or determine its impossibility) is developed in [Sh:a]. It is…

Let $A$ be a hereditary algebra. We construct a fundamental domain for the cluster category of $A$ inside the category of modules over the duplicated algebra $\bar{A}$ of $A$. We then prove that there exists a bijection between the tilting…

We generalize the small object argument in order to allow for its application to proper classes of maps (as opposed to sets of maps in Quillen's small object argument). The necessity of such a generalization arose with appearance of several…

We develop algebraic models of simple type theories, laying out a framework that extends universal algebra to incorporate both algebraic sorting and variable binding. Examples of simple type theories include the unityped and simply-typed…

Let $k$ be a field of characteristic $0$, let $\mathsf{C}$ be a finite split category, let $\alpha$ be a 2-cocycle of $\mathsf{C}$ with values in the multiplicative group of $k$, and consider the resulting twisted category algebra…

We define the notion of an additive model category, and we prove that any additive, stable, combinatorial model category has a natural enrichment over symmetric spectra based on simplicial abelian groups. As a consequence, every object in…

In this article we study the properties of preprojective algebras of representation finite species. To understand the structure of a preprojective algebra, one often studies its Nakayama automorphism. A complete description of the Nakayama…

Implicative algebras have been recently introduced by Miquel in order to provide a unifying notion of model, encompassing the most relevant and used ones, such as realizability (both classical and intuitionistic), and forcing. In this work,…

The aim of this article is to study certain categorical-algebraic frameworks for basic homological algebra, introduced in arXiv:2404.15896, with the aim of better understanding the differences between them. We focus on homological…

This book is an introductory course to basic commutative algebra with a particular emphasis on finitely generated projective modules, which constitutes the algebraic version of the vector bundles in differential geometry. We adopt the…

Following ideas of Lawvere and Linton we prove that classical varieties are precisely the exact categories with a varietal generator. This means a strong generator which is abstractly finite and regularly projective. An analogous…

Phylogenetic algebraic geometry is concerned with certain complex projective algebraic varieties derived from finite trees. Real positive points on these varieties represent probabilistic models of evolution. For small trees, we recover…

Let $K$ be a normal subgroup of the finite group $H$. To a block of a $K$-interior $H$-algebra we associate a group extension, and we prove that this extension is isomorphic to an extension associated to a block given by the Brauer…

A field algebra is a ``non-commutative'' generalization of a vertex algebra. In this paper we develop foundations of the theory of field algebras.

For a certain class of (nonunital) subalgebras of deformed preprojective algebra of affine type we describe their centers as certain deformation of Kleinian singularity and find their PI-degree. These results can be applied to algebras…

In this paper, we study Heisenberg vertex algebras over fields of prime characteristic. The new feature is that the Heisenberg vertex algebras are no longer simple unlike in the case of characteristic zero. We then study a family of simple…

We consider, for each exchange matrix B, a category of geometric cluster algebras over B and coefficient specializations between the cluster algebras. The category also depends on an underlying ring R, usually the integers, rationals, or…

We define the preprojective algebra of a finite EI quiver. We prove that it is isomorphic to a centain tensor algebra. For a finite EI quiver of Cartan type, we prove that the corresponding preprojective algebra is isomorphic to the…