Related papers: Derived tame local and two-point algebras

Two extension problems are solved. First, the class of locally matricial algebras over an arbitrary field is closed under extensions. Second, the class of locally finite dimensional semisimple algebras over a fixed field is closed under…

We provide a clarification of the classification of two-dimensional algebras over an arbitrary base field. Using this clarification, we determine the number of non-isomorphic two-dimensional algebras over a finite field.

As the first attempt to classify $\tau$-tilting finite two-point algebras, we have determined the $\tau$-tilting finiteness for minimal wild two-point algebras and some tame two-point algebras.

In this paper we investigate the problem of which Lie algebras appear as the derived algebra of a Lie algebra. We present new results that further develop this study and address two questions raised in a paper concerned with the…

We classify the representation type of the descent algebras of type $\A$ in the positive characteristic case. The algebras have finite representation type only for a few small degrees; otherwise, they are wild. Our main reduction method…

The present paper is devoted to study 2-local derivations on infinite-dimensional Lie algebras over a field of characteristic zero. We prove that all 2-local derivations on the Witt algebra as well as on the positive Witt algebra are…

Twisted loop algebras of the second kind are infinite-dimensional Lie algebras that are constructed from a semisimple Lie algebra and an automorphism on it of order at most $2$. They are examples of equivariant map algebras. The…

We prove that any derived equivalence between derived discrete algebras is standard, i.e.\ is isomorphic to the derived tensor product by a two-sided tilting complex.

A complete classification and character formulas for finite-dimensional irreducible representations of the rational Cherednik algebra of type A is given. Less complete results for other types are obtained. Links to the geometry of affine…

We complete a classification of the two-vertex geometrically irreducible algebras. We also classify the algebras in new classes of hom- and ext-irreducible algebras.

We construct some irreducible representations of the Leavitt path algebra of an arbitrary quiver. The constructed representations are associated to certain algebraic branching systems. For a row-finite quiver, we classify algebraic…

In the paper we give a complete classification of $2$-dimensional evolution algebras over algebraically closed fields, describe their groups of automorphisms and derivation algebras.

In the present paper we prove that every local and $2$-local derivation on conservative algebras of $2$-dimensional algebras are derivations. Also, we prove that every local and $2$-local automorphism on conservative algebras of…

We classify pointed Hopf algebras of discrete corepresentation type over an algebraically closed field K with characteristic zero. For such algebras $H$, we explicitly determine the algebra structure up to isomorphism for the link…

We classify the irreducible finite-dimensional representations of the twisted quantum affine algebras.

In our previous work arXiv:1306.1770, we found all Borel-Schur algebra of finite representation type. In the present article, we determine which Borel-Schur algebras of infinite representation type are tame, and which are wild.

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 give a complete description of the derived equivalence normal forms of all one-parametric selfinjective algebras over algebraically closed fields which admit simply connected Galois coverings. As a consequence, a description of the…

We classify derived-discrete algebras over the real numbers up to Morita equivalence, using the classification of complex derived-discrete algebras in [{\sc D. Vossieck}, {\em The algebras with discrete derived category}, J. Algebra {\bf…

We study the representation theory of finite-dimensional $\omega$-Lie algebras over the complex field. We derive an $\omega$-Lie version of the classical Lie's theorem, i.e., any finite-dimensional irreducible module of a soluble…