Related papers: Some algebras that are not silting connected
To a regular projection of a knot we associate a finite dimensional non-commutative associative algebra which is self-injective and special biserial.
We give a proof, based on the rigidity of tilting complexes, that the class of self-injective finite-dimensional algebras over an algebraically closed field is closed under derived equivalence.
We study cluster tilting modules in mesh algebras of Dynkin type, providing a new proof for their existence. In all but one case, we show that these are precisely the maximal rigid modules, and that they are equivariant for a certain…
Hilbert evolution algebras generalize evolution algebras through a framework of Hilbert spaces. In this work we focus on infinite-dimensional Hilbert evolution algebras and their representation through a suitably defined weighted digraph.…
We study the transfer of (co)silting objects in derived categories of module categories via the extension functors induced by a morphism of commutative rings. It is proved that the extension functors preserve (co)silting objects of…
In this paper using a geometric model we show that there is a presilting complex over a finite dimensional algebra, which is not a direct summand of a silting complex.
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…
Given a measure preserving transformation $T$ on a Lebesgue $\sigma$ algebra, a complete $T$ invariant sub $\sigma$ algebra is said to split if there is another complete $T$ invariant sub $\sigma$ algebra on which $T$ is Bernoulli which is…
We develop the theory of ``branch algebras'', which are infinite-dimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting…
In this paper we produce noncommutative algebras derived equivalent to deformations of schemes with tilting bundles. We do this in two settings, first proving that a tilting bundle on a scheme lifts to a tilting bundle on an infinitesimal…
There are well-known constructions relating ring epimorphisms and tilting modules. The new notion of silting module provides a wider framework for studying this interplay. To every partial silting module we associate a ring epimorphism…
We consider an evolution algebra which corresponds to a bisexual population with a set of females partitioned into finitely many different types and the males having only one type. We study basic properties of the algebra. This algebra is…
Let $A$ be a semiprime 2 and 3-torsion free non-commutative associative algebra. We show that the Lie algebra $\der(A)$ of (associative) derivations of $A$ is strongly non-degenerate, which is a strong form of semiprimeness for Lie…
In this paper we classify invariant noncommutative connections in the framework of the algebra of endomorphisms of a complex vector bundle. It has been proven previously that this noncommutative algebra generalizes in a natural way the…
Let $A$ be a finite dimensional hereditary algebra over an algebraically closed field $k$, $A^{(m)}$ be the $m$-replicated algebra of $A$ and $\mathscr{C}_{m}(A)$ be the $m$-cluster category of $ A$. We investigate properties of complements…
We consider a class of extensions of associative algebras, which we refer to as ``strongly proj-bounded extensions''. We prove that the finiteness of the left global dimension and the support of the Hochschild homology is preserved by…
Given a Hopf algebra H, we study modules and bimodules over an algebra A that carry an H-action, as well as their morphisms and connections. Bimodules naturally arise when considering noncommutative analogues of tensor bundles. For…
We study certain "\sigma-commuting varieties" associated with a pair of commuting involutions of a semisimple Lie algebra $\g$. The usual commuting variety of $\g$ and commuting varieties related to one involution are particular cases of…
We confirm a conjecture by Lekili and Polishchuk that the geometric invariants which they construct for homologically smooth graded (not necessarily proper) gentle algebras form a complete derived invariant. Hence, we obtain a complete…
A non associative, noncommutative algebra is defined that may be interpreted as a set of vector modules over a noncommutative surface of rotation. Two of these vector modules are identified with the analogues of the tangent and cotangent…