相关论文: Toupie algebra, some examples of laura algebras

In this paper, we propose a generalization for the class of laura algebras, which we call almost laura. We show that this new class of algebras retains most of the essential features of laura algebras, especially concerning the important…

We give a new characterization of tilted algebras by the existence of certain special subquivers in their Auslander-Reiten quiver. This result includes the existent characterizations of this kind and yields a way to obtain more tilted…

We call an $\mathbb{R}$-algebra locally complexified-gentle if it becomes a locally gentle $\mathbb{C}$-algebra up to Morita equivalence after complexification. We use modulated quivers to introduce two types of locally complexified-gentle…

A cluster tilted algebra is known to be gentle if and only if it is cluster tilted of Dynkin type $\bbA$ or Euclidean type $\tilde{\bbA}$. We classify all finite dimensional algebras which are derived equivalent to gentle cluster tilted…

Motivated by the structure of the algebras associated to the blocks of the BGG-category O we define a subclass of quasi-hereditary algebras called 1-quasi-hereditary. Many properties of these algebras only depend on the defining partial…

In this short paper we prove that a finite dimensional algebra is hereditary if and only if there is no loop in its ordinary quiver and every $\tau$-tilting module is tilting.

We give a simple combinatorial criterion allowing to recognize whether a string (or, more generally, a special biserial) algebra is a laura algebra or not. We also show that a special biserial algebra is laura if and only if it has a finite…

Let $A$ be a partial *-algebra endowed with a topology $\tau$ that makes it into a locally convex topological vector space $A[\tau]$. Then $A$ is called a topological partial *-algebra if it satisfies a number of conditions, which all…

We classify (possibly non commutative) algebras of low rank over a domain R. We first review results for algebras of rank 2 and for finite-dimensional division algebras over the real numbers. These results motivate us to consider which…

This paper provides the next step towards classification of algebras of generalized quaternion type. Previously algebras with 2-regular Gabriel quiver were classified (a quiver is 2-regular if at each vertex, two arrows start and two arrows…

In this paper we study the lattice of restricted subalgebras of a restricted Lie algebra. In particular, we consider those algebras in which this lattice is dually atomistic, lower or upper semimodular, or in which every restricted…

In this paper we revisit the notion of strict laura algebras through the lens of $\tau$-tilting theory to define the family of algebras determined by $\tau$-slices. We show that the representation dimension of every algebra determined by…

For simply-laced quivers, we consider the fixed-point subalgebra of the quiver Hecke algebra under the homogeneous sign map. This leads to a new family of algebras we call alternating quiver Hecke algebras. We give a basis theorem and a…

Given a simple finite-dimensional Lie algebra and an automorphism of finite order, one defines the notion of a twisted toroidal Lie algebra. In this paper, we construct representations of twisted toroidal Lie algebras from twisted modules…

We introduce tabular algebras, which are simultaneous generalizations of cellular algebras (in the sense of Graham-Lehrer) and table algebras (in the sense of Arad-Blau). We show that if a tabular algebra is equipped with a certain kind of…

The quasi-filiform Lie algebras of nonzero rank are described. The classifications of filiform and quasi-filiform naturally graded algebras are corrected.

Some examples are given of finite dimensional Lie bialgebras whose brackets and cobrackets are determined by pairs of $r$-matrices.

We apply the notion of a full convex subcategory to a wide range of algebras including tilted, quasi-tilted, shod, weakly shod, left and right glued, laura, simply connected, strongly simply connected, left supported, and cluster-tilted. In…

A Lie algebra is said to be quadratic if it admits a symmetric invariant and non-degenerated bilinear form. Semisimple algebras with the Killing form are examples of these algebras, while orthogonal subspaces provide abelian quadatric…

We give a full classification of Lie algebras of specific type in complexified Clifford algebras. These sixteen Lie algebras are direct sums of subspaces of quaternion types. We obtain isomorphisms between these Lie algebras and classical…