Related papers: Classifying tilting complexes over preprojective a…
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 study the general properties of commutative differential graded algebras in the category of representations over a reductive algebraic group with an injective central cocharacter. Besides describing the derived category of differential…
We give a classification theorem for a relevant class of $t$-structures in triangulated categories, which includes in the case of the derived category of a Grothendieck category, the $t$-structures whose hearts have at most $n$ fixed…
We characterize twisted right-angled Artin groups whose finitely generated subgroups are also twisted right-angled Artin groups. Additionally, we give a classification of coherence within this class of groups in terms of the defining graph.…
We explain the construction of minimal tilting complexes for objects of highest weight categories and we study in detail the minimal tilting complexes for standard objects and simple objects. For certain categories of representations of…
We describe the fine (group) gradings on the Heisenberg algebras, on the Heisenberg superalgebras and on the twisted Heisenberg algebras. We compute the Weyl groups of these gradings. Also the results obtained respect to Heisenberg…
We study the stable category of the factor algebra of the preprojective algebra associated with an element $w$ of the Coxeter group of a quiver. We show that there exists a silting object $M(\bf{w})$ of this category associated with each…
We propose a definition of Coxeter-Dynkin algebras of canonical type generalising the definition as a path algebra of a quiver. Moreover, we construct two tilting objects over the squid algebra - one via generalised APR-tilting and one via…
The present paper is a continuation of [5], where Lie bialgebra structures on g[u] were studied. These structures fall into different classes labelled by the vertices of the extended Dynkin diagram of g. In [5] the Lie bialgebras…
In association with a finite dimensional algebra A of global dimension two, we consider the endomorphism algebra of A, viewed as an object in the triangulated hull of the orbit category of the bounded derived category, in the sense of…
We classify $n$-representation infinite algebras $\Lambda$ of type \~A. This type is defined by requiring that $\Lambda$ has higher preprojective algebra $\Pi_{n+1}(\Lambda) \simeq k[x_1, \ldots, x_{n+1}] \ast G$, where $G \leq…
We present a classification of characteristic Dynkin diagrams for the $A_N$, $B_N$, $C_N$ and $D_N$ algebras. This classification is related to the classification of \cw(\cg,\ck) algebras arising from non-Abelian Toda models, and we argue…
Comparing the bounded derived categories of an algebra and of the endomorphism algebra of a given support {\tau}-tilting module, we find a relation between the derived dimensions of an algebra and of the endomorphism algebra of a given…
For an exact category $\mathcal{E}$ with enough projectives and with a $d\mathbb{Z}$-cluster tilting subcategory, we show that the singularity category of $\mathcal{E}$ admits a $d\mathbb{Z}$-cluster tilting subcategory. To do this we…
In the acyclic case, we establish a one-to-one correspondence between the tilting objects of the cluster category and the clusters of the associated cluster algebra. This correspondence enables us to solve conjectures on cluster algebras.…
The Krein--Tannaka duality for compact groups was a generalization the Pontryagin--Van Kampen duality for locally compact abelian groups and a remote predecessor of the theory of tensor categories. It is less known that it found…
All quasi-affine connected Generalized Dynkin Diagrams with rank $> 5$ are found. All quasi-affine Nichols (Lie braided) algebras with rank $> 5$ are also found.
We investigate the notion of associated graded coalgebra (algebra) of a bialgebra with respect to a subbialgebra (quotient bialgebra) and characterize those which are bialgebras of type one in the framework of abelian braided monoidal…
In this paper, we introduce a new generating function called $d$-polynomial for the dimensions of $\tau$-tilting modules over a given finite dimensional algebra. Firstly, we study basic properties of $d$-polynomials and show that it can be…
For a semisimple Lie algebra over the complex numbers, Dynkin (1952) developed an algorithm to classify the regular semisimple subalgebras, up to conjugacy by the inner automorphism group. For a graded semisimple Lie algebra over the…