Related papers: From support $\tau$-tilting posets to algebras
The notion of (semi)bricks, regarded as a generalization of (semi)simple modules, appeared in a paper of Ringel in 1976. In recent years, there has been several new developments motivated by links to {\tau}-tilting theory studied by…
We characterize $\tau$-tilting modules as $1$-tilting modules over quotient algebras satisfying a tensor-vanishing condition, and characterize $1$-tilting modules as $\tau$-tilting modules satisfying a ${\rm Tor}^1$-vanishing condition. We…
We begin a study of torsion theories for representations of an important class of associative algebras over a field which includes all finite W-algebras of type A, in particular the universal enveloping algebra of gl(n) (or sl(n)) for all…
A skew Calabi-Yau algebra is a generalization of a Calabi-Yau algebra which allows for a non-trivial Nakayama automorphism. We prove three homological identities about the Nakayama automorphism and give several applications. The identities…
For a fixed finite dimensional algebra $A$, we study representation embeddings of the form $mod(B)\rightarrow mod(A)$. Such an embedding is called homological, if it induces an isomorphism on all Ext-groups and weakly homological, if only…
If $\Delta$ and $\Gamma$ are two derivations of a commutative algebra $A$ such that $\Delta\Gamma-\Gamma\Delta=\Delta$ is locally nilpotent, one can endow $A$ with a new product $\ast$ whose filtered semiclassical limit is the Poisson…
Let $\Lambda$ be a 1-Auslander-Gorenstein Algebra. We give a necessary and sufficient condition for $\Lambda$ to be a tilted algebra.
In this short note, we explain how the main results in "$\tau$-tilting theory" by Adachi-Iyama-Reiten follow from the results in Section 5 of "General presentations of algebras" by Derksen-Fei.
Let $\mathcal{E}=(\mathcal{A},\mathcal{S})$ be an exact category with enough projectives $\mathcal{P}$. We introduce the notion of support $\tau$-tilting subcategories of $\mathcal{E}$. It is compatible with existing definitions of support…
In representation theory of finite-dimensional algebras, (semi)bricks are a generalization of (semi)simple modules, and they have long been studied. The aim of this paper is to study semibricks from the point of view of $\tau$-tilting…
Brauer graph algebras form a classical class of symmetric algebras with well-structured combinatorial properties and geometric models. Recently, they have been generalized to biserial fractional Brauer graph algebras, which can be regarded…
In this paper we study the (co)homology of Tanabe algebras, which are a family of subalgebras of the partition algebras exhibiting a Schur-Weyl duality with certain complex reflection groups. The homology of the partition algebras has been…
Let $\Lambda$ be an algebra with a indecomposable projective-injective module. Adachi gave a method to construct the Hasse quiver of support $\tau$-tilting $\Lambda$-modules. In this paper, we will show that it can be restricted to…
Generalized orthomodular posets were introduced recently by D. Fazio, A. Ledda and the first author of the present paper in order to establish a useful tool for studying the logic of quantum mechanics. They investigated structural…
Gluing techniques with respect to a recollement have long been studied. Recently, ladders of recollements of abelian categories were introduced as important tools. We present explicit constructions of gluing of support $\tau$-tilting…
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…
The Kadar--Yu algebras are a physically motivated sequence of towers of algebras interpolating between the Brauer algebras and Temperley--Lieb algebras. The complex representation theory of the Brauer and Temperley--Lieb algebras is now…
We introduce the category of Heyting frames and show that it is equivalent to the category of Heyting algebras and dually equivalent to the category of Esakia spaces. This provides a frame-theoretic perspective on Esakia duality for Heyting…
Inspired by Kalton and Wood's work on group algebras, we describe almost completely contractive algebra homomorphisms from Fourier algebras into Fourier-Stieltjes algebras (endowed with their canonical operator space structure). We also…
Homological smoothness and twisted Calabi-Yau property of generalized Weyl algebras over polynomial algebras in two variables is studied. A necessary and sufficient condition to be homologically smooth is given. The Nakayama automorphisms…