Related papers: 3-Preprojective Algebras of Type D

The class of finitely presented algebras over a field $K$ with a set of generators $a_{1},..., a_{n}$ and defined by homogeneous relations of the form $a_{1}a_{2}... a_{n} =a_{\sigma (a)} a_{\sigma (2)} ... a_{\sigma (n)}$, where $\sigma$…

We describe pretty examples of derived equivalences and autoequivalences of Calabi-Yau threefolds arising from pencils of cubic fourfolds. The cubic fourfolds are chosen to be special, so they have an associated K3 surface. Thus a pencil…

Let A=k+A_1+A_2.... be a connected graded, noetherian k-algebra that is generated in degree one over an algebraically closed field k. Suppose that the graded quotient ring Q(A) has the form Q(A)=k(Y)[t,t^{-1},sigma], where sigma is an…

In a paper by Su and Zhao, the Lie algebra $A[D]=A\otimes F[D]$ of Weyl type was defined and studied, where $A$ is a commutative associative algebra with an identity element over a field $F$ of arbitrary characteristic, and $F[D]$ is the…

We study tilting complexes over preprojective algebras of Dynkin type. We classify all tilting complexes by giving a bijection between tilting complexes and the braid group of the corresponding folded graph. In particular, we determine the…

Loday's dendriform algebras and its siblings pre-Lie and zinbiel have received attention over the past two decades. In recent literature, there has been interest in a generalization of these types of algebra in which each individual…

This is the second in a series of papers which give an explicit description of the reconstruction algebra as a quiver with relations; these algebras arise naturally as geometric generalizations of preprojective algebras of extended Dynkin…

In this paper the authors investigate the $q$-Schur algebras of type B that were constructed earlier using coideal subalgebras for the quantum group of type A. The authors present a coordinate algebra type construction that allows us to…

We are going to determine all the self-injective cluster tilted algebras. All are of finite representation type and special biserial.

In this paper, we introduce the notion of a pre-Lie 2-algebra, which is a categorification of a pre-Lie algebra. We prove that the category of pre-Lie 2-algebras and the category of 2-term pre-Lie$_\infty$-algebras are equivalent. We…

In this article we prove that double quasi-Poisson algebras, which are non-commutative analogues of quasi-Poisson manifolds, naturally give rise to pre-Calabi-Yau algebras. This extends one of the main results in [11] (see also [10]), where…

We study some conjectures about Chow groups of varieties of geometric genus one. Some examples are given of Calabi-Yau threefolds where these conjectures can be verified, using the theory of finite-dimensional motives.

We introduce a family of polynomials in $q^2$ and four variables associated with the quantized algebra of functions $A_q(C_2)$. A new formula is presented for the recent solution of the 3D reflection equation in terms of these polynomials…

We give a new type of Schur-Weyl duality for the representations of a family of quantum subgroups and their centralizer algebra. We define and classify singly-generated, Yang-Baxter relation planar algebras. We present the skein theoretic…

In this paper, we explicitly determine all $\mathcal{O}$-operators with respect to the adjoint representation of 3-dimensional complex 3-Lie algebras. Furthermore, we provide the induced 3-Pre-Lie algebra structures and the corresponding…

Some basic facts about the prepotential in the SW/Whitham theory are presented. Consideration begins from the abstract theory of quasiclassical $\tau$-functions , which uses as input a family of complex spectral curves with a meromorphic…

A family of solvable self-dual Lie algebras is presented. There exist a few methods for the construction of non-reductive self-dual Lie algebras: an orthogonal direct product, a double-extension of an Abelian algebra, and a Wigner…

Motivated by the relation between Schur algebra and the group algebra of a symmetric group, along with other similar examples in algebraic Lie theory, Min Fang and Steffen Koenig addressed some behaviour of the endomorphism algebra of a…

We show that the stable module categories of certain selfinjective algebras of finite representation type having tree class A_n, D_n, E_6, E_7 or E_8 are triangulated equivalent to u-cluster categories of the corresponding Dynkin type. The…

We consider a finite dimensional strongly $G$-graded algebra $A$ with { self-injective} $1$-component $B$, and in our main result we prove that the induction from $B$ to $A$ of a basic support $\tau$-tilting pair of $B$-modules is a support…