相关论文: On the Dimensions of Path Algebras
It is shown that the derived dimension of any representation-finite Artin algebra is at most one.
The representation dimension of an artin algebra as introduced by M.Auslander in his Queen Mary Notes is the minimal possible global dimension of the endomorphism ring of a generator-cogenerator. The paper is based on two texts written in…
This is an overview article on finite-dimensional algebras and quivers, written for the Encyclopedia of Mathematical Physics. We cover path algebras, Ringel-Hall algebras and the quiver varieties of Lusztig and Nakajima.
This is a companion paper of arXiv:1901.09461, where different notions of dimension for triangulated categories are discussed. Here we compute dimensions for some examples of triangulated categories and thus illustrate and motivate material…
We consider selfinjective Artin algebras whose cohomology groups are finitely generated over a central ring of cohomology operators. For such an algebra, we show that the representation dimension is strictly greater than the maximal…
Let $K$ be a field, $Q$ a quiver, and $\mathcal{A}$ the ideal of the path algebra $KQ$ that is generated by the arrows of $Q$. We present old and new results about the representation theories of the truncations $KQ/\mathcal{A}^L$, $L \in…
In this article we obtain lower and upper bounds for global dimensions of a class of artinian algebras in terms of global dimensions of a finite subset of their artinian subalgebras. Finding these bounds for the global dimension of an…
We study finite dimensional representations of the quantum affine algebra, using geometry of quiver varieties introduced by the author. As an application, we obtain character formulas expressed in terms of intersection cohomologies of…
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…
There is a well-known class of algebras called Igusa-Todorov algebras which were introduced in relation to finitistic dimension conjecture. As a generalization of Igusa-Todorov algebras, the new notion of $(m,n)$-Igusa-Todorov algebras…
We show that the path algebra of a quiver satisfies the same polynomial identities of an algebra of matrices, if any. In particular, the algebra of nxn matrices is PI-equivalent to the path algebra of the oriented cycle with n vertices.
This is a survey article for "Handbook of Linear Algebra", 2nd ed., Chapman & Hall/CRC, 2014. An informal introduction to representations of quivers and finite dimensional algebras from a linear algebraist's point of view is given. The…
Let $A$ be an Artin algebra. We investigate subalgebras of $A$ with certain conditions and obtain some classes of algebras whose finitistic dimensions are finite.
We study the representation dimension of the class of algebras known as quantum complete intersections. For such an algebra, we show that the representation dimension is at most twice its codimension. Moreover, we show that the…
We study the connection between two combinatorial notions associated to a quiver: the quiver algebra and the path coalgebra. We show that the quiver coalgebra can be recovered from the quiver algebra as a certain type of finite dual, and we…
In this survey we discuss the results on the finitistic dimension of various stratified algebras. We describe what is already known, present some recent estimates, and list some open problems.
We study endomorphisms and derivations of infinite dimensional cyclic Leibniz algebra.
We characterize pairs (Q,d) consisting of a quiver Q and a dimension vector d, such that over a given algebraically closed field k there are infinitely many representations of Q of dimension vector d. We also present an application of this…
We provide a topological characterization of quivers whose path algebra satisfies a polynomial identity. This class includes the oriented cycle and acyclic quivers and, in the latter case, we describe the associated T-ideal. We introduce a…
The theory of path algebras is usually circunscripted to the study of representations, usually linked to finite graphs. In our work, we focus on studying the structure of path algebras over a field associated to arbitrary graphs. We…