Related papers: Algebras of Derived dimension zero

We determine the derived representation types of algebras with radical square zero and give a description of the indecomposable objects in their bounded derived categories.

It is shown that the derived dimension of any representation-finite Artin algebra is at most one.

We construct an algebra of dimension $2^{\aleph_0}$ consisting only of functions which in no point possess a finite one-sided derivative. We further show that some well known nowhere differentiable functions generate algebras, which contain…

We study the algebras of derivations of nilpotent Leibniz algebras of low dimensions.

A complete classifications, up to isomorphism, of two-dimensional associative and diassociative algebras over any basic field are given.

For an arbitrary octonion algebra, we determine all subalgebras. It turns out that every subalgebra of dimension less than four is associative, while every subalgebra of dimension greater than four is not associative. In any split octonion…

We determine some of the derived equivalences of a class of gentle algebras called surface algebras. These algebras are constructed from an unpunctured Riemann surface of genus 0 with boundary and marked points by introducing cuts in…

Realizations of four dimensional Lie algebras as vector fields in the plane are explicitly constructed. Fourth order ordinary differential equations which admit such Lie symmetry algebras are derived. The route to their integration is…

A complete classification of two-dimensional algebras over algebraically closed fields is provided

It is well known that a finite-dimensional Lie algebra over a field of characteristic zero is simple exactly when its derivation algebra is simple. In this paper we characterize those Lie algebras of arbitrary dimension over any field that…

In this work we study Leibniz algebras whose second-maximal subalgebras are ideals. We provide a classification based on solvability, nilpotency, and the size of the derived algebra. We give specific descriptions of those Leibniz algebras…

In this paper, we classify all capable nilpotent Lie algebras with derived subalgebra of dimension at most 1.

We describe, in terms of generators and relations, the derived Hall algebras associated to the one-cycle gentle algebras of infinite global dimension.

We construct a nil algebra over a countable field which has finite but non-zero Gelfand-Kirillov dimension.

We give a complete description of the varieties of associative algebras over a field of characteristic zero which satisfy a polynomial identity of third degree.

For each complex 8-dimensional filiform Lie algebra we find another non isomorphic Lie algebra that degenerates to it. Since this is already known for nilpotent Lie algebras of rank $\ge 1$, only the caracteristically nilpotent ones should…

The space of derivations of finite dimensional evolution algebras associated to graphs over a field with characteristic zero has been completely characterized in the literature. In this work we generalize that characterization by describing…

We prove that every finite dimensional algebra over an algebraically closed field is either derived tame or derived wild. We also prove that any deformation of a derived tame algebra is derived tame.

We present a list of all isomorphism classes of nonsolvable Lie algebras of dimension less than 7 over a finite field.

We give an explicit description of the Lie algebra of derivations for a class of infinite dimensional algebras which are given by \'etale descent. The algebras under consideration are twisted forms of central algebras over rings, and…