Related papers: Two-term partial tilting complexes over Brauer tre…

We show how to integrate a weak morphism of Lie algebra crossed-modules to a weak morphism of Lie 2-groups. To do so we develop a theory of butterflies for 2-term L_infty algebras. In particular, we obtain a new description of the…

Using the algebraic classification of all $2$-dimensional algebras, we give the algebraic classification of all $2$-dimensional rigid, conservative and terminal algebras over an algebraically closed field of characteristic 0. We have the…

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 introduce the notion of AIR tilting subcategories of extended hearts of $t$-structures on a triangulated category associated with silting subcategories. This notion generalizes $\tau_{[d]}$-tilting pairs of extended finitely generated…

We describe the derived Picard groups and two-term silting complexes for quasi-hereditary algebras with two simple modules. We also describe by quivers with relations all algebras derived equivalent to a quasi-hereditary algebra with two…

The radical of the Brauer algebra B_f^x is known to be non-trivial when the parameter x is an integer subject to certain conditions (with respect to f). In these cases, we display a wide family of elements in the radical, which are…

We investigate the rings of semi-invariants for tame string algebras A(n) of non-polynomial growth. We are interested in dimension vectors of band modules. We use geometric technique related to the description of coordinate rings on…

We introduce two classes of algebras coming from partial triangulations of marked surfaces. The first one, called frozen algebra of a partial triangulation, is generally of infinite rank and contains frozen Jacobian algebras of…

We describe how traceless projection of tensors of a given rank can be constructed in a closed form. On the way to this goal we invoke the representation theory of the Brauer algebra and the related Schur-Weyl dualities. The resulting…

In this paper, we study the relationship between equivalences of noncommutative projective schemes and cluster tilting modules. In particular, we prove the following result. Let $A$ be an AS-Gorenstein algebra of dimension $d\geq 2$ and…

We study some non-semisimple representations of affine Temperley--Lieb algebras and related cellular algebras. In particular, we classify extensions between simple standard modules. Moreover, we construct a completion which is an infinite…

The class in the Brauer group of a quaternion algebra over a field is 2-torsion. We study the following question: Which 2-torsion elements of the Brauer group of a complex function field are representable by quaternion algebras? Using…

We study the properties of tilting modules in the context of properly stratified algebras. In particular, we answer the question when the Ringel dual of a properly stratified algebra is properly stratified itself, and show that the class of…

Many important problems in extremal combinatorics can be stated as certifying polynomial inequalities in graph homomorphism numbers, and in particular, many ask to certify pure binomial inequalities. For a fixed collection of graphs…

We give a bijection between the tilting complexes in the bounded homotopy category of the Auslander algebra of the truncated polynomial ring and ZxB where B is the Artin braid goup of type A with n-1 generators. The tilting complexes have…

We construct a new class of symmetric algebras of tame representation type that are also the endomorphism algebras of cluster tilting objects in 2-Calabi-Yau triangulated categories, hence all their non-projective indecomposable modules are…

Let $A$ be the one point extension of an algebra $B$ by a projective $B$-module. We prove that the extension of a given support $\tau$-tilting $B$-module is a support $\tau$-tilting $A$-module; and, conversely, the restriction of a given…

We study infinite string modules that are bricks over some gentle algebras. In particular, we first give a complete classification of these modules over the double-Kronecker gentle algebra and prove that each family is in bijection with a…

In this paper, we give a complete classification of extensions of finite irreducible conformal modules over rank two Lie conformal algebras.

Relying on the classification of the indecomposable liftable modules in arbitrary blocks with non-trivial cyclic defect groups we give a complete classification of the trivial source modules lying in such blocks, describing in particular…