Related papers: Three kinds of mutation
We classify Nichols algebras of irreducible Yetter-Drinfeld modules over nonabelian groups satisfying an inequality for the dimension of the homogeneous subspace of degree two. All such Nichols algebras are finite-dimensional, and all known…
We study the projective dimensions of the restriction of functors Hom(-,X) to a contravariantly finite rigid subcategory T of a triangulated category C. We show that the projective dimension of Hom(-,X)|T is at most one if and only if there…
We introduce the notion of composition series of triangulated categories, which generalizes full exceptional sequences. The lengths of composition series yield invariants for triangulated categories. We study composition series of derived…
For an acyclic quiver $Q$ and a finite-dimensional algebra $A$, we give a unified form of the indecomposable injective objects in the monomorphism category ${\rm Mon}(Q,A)$ and prove that ${\rm Mon}(Q, A)$ has enough injective objects. As…
We give a geometric realization of a subcategory of the $m$-cluster category $\mathcal{C}^m$ of type $\widetilde{A}_{p,q}$, by using $(m+2)$-angulations of an annulus with $p+q$ marked points. We also give a bijection between an equivalence…
In this paper we classify, up to isomorphism, the superinvolutions on algebras of upper block-triangular matrices over an algebraically closed field of characteristic different from $2$.
Using approximations, we give several characterizations of separability of bimodules. We also discuss how separability properties can be used to transfer some representation theoretic properties from one ring to another one: contravariant…
Cluster algebras have recently become an important player in mathematics and physics. In this work, we investigate them through the lens of modern data science, specifically with techniques from network science and machine learning. Network…
In this work we study the connection between iterated tilted algebras and m-cluster tilted algebras. We show that an iterated tilted algebra induces an m-cluster tilted algebra. This m-cluster tilted algebra can be seen as a trivial…
A self-contained introduction to infinite dimensional representations over a tame hereditary algebra is provided, assuming a basic knowledge of the category of finite dimensional representations. This includes a complete description of all…
An involution is usually defined as a mapping that is its own inverse. In this paper, we study quaternion involutions that have the additional properties of distribution over addition and multiplication. We review formal axioms for such…
We develop a structure theory for two classes of infinite dimensional modules over tame hereditary algebras: the Baer modules, and the Mittag-Leffler ones.
The irreducible alternative superbimodules are studied. The complete classification is obtained for even bimodules of arbitrary dimension and for finite-dimensional irreducible superbimodules over an algebraically closed field.
Let $X$ be a $2$-dimensional subshift of finite type generated by a finite set of forbidden blocks (of finite size). We give an algorithm for generating the elements of the shift space using sequence of finite matrices (of increasing size).…
Spectral properties of many finite convolution integral operators have been understood by finding differential operators that commute with them. In this paper we compile a complete list of such commuting pairs, extending previous work to…
A hereditary property of quivers is a property preserved by restriction to any full subquiver. Similarly, a mutation-invariant property of quivers is a property preserved by mutation. Using forks, a class of quivers developed by M.…
Two models of candidates for hereditary symmetry operators are proposed and thus many nonlinear systems of evolution equations possessing infinitely many commutative symmetries may be generated. Some concrete structures of hereditary…
We classify three dimensional evolution algebras over a field having characteristic different from 2 and in which there are roots of orders 2, 3 and 7.
We study higher cluster tilting objects in generalized higher cluster categories arising from dg algebras of higher Calabi-Yau dimension. Taking advantage of silting mutations of Aihara-Iyama, we obtain a class of $m$-cluster tilting…
Given a tilting object of the derived category of an abelian category of finite global dimension, we give (under suitable finiteness conditions) a bound for the global dimension of its endomorphism ring.