相关论文: Delooping Level of Nakayama algebras

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.

A new (in)finite dimensional algebra which is a fundamental dynamical symmetry of a large class of (continuum or lattice) quantum integrable models is introduced and studied in details. Finite dimensional representations are constructed and…

The Nakayama permutations of two derived equivalent, self-injective Artin algebras are conjugate. A different but elementary approach is given to showing that the weak symmetry and self-injectivity of finite-dimensional algebras over an…

We consider a natural generalisation of symmetric Nakayama algebras, namely, symmetric special biserial algebras with at most one non-uniserial indecomposable projective module. We describe the basic algebras explicitly by quiver and…

We give a survey of recent results related to the problem of characterizing finite-dimensional division algebras by the set of isomorphism classes of their maximal subfields. We also discuss various generalizations of this problem and some…

We consider the question of which zero-dimensional schemes deform to a collection of distinct points; equivalently, we ask which Artinian k-algebras deform to a product of fields. We introduce a syzygetic invariant which sheds light on this…

We introduce the notion of radical preservation and prove that a radical-preserving homomorphism of left artinian rings of finite projective dimension with superfluous kernel reflects the finiteness of the little finitistic, big finitistic…

The Satake compactification of the moduli space of principally polarized abelian surfaces with a level two structure has a degree 8 endomorphism. The aim of this paper is to show that this result can be extended to other modular threefolds.…

We show that the finite-dimensional fundamental module over a quantized affine algebra is isomorphic to a Demazure module of a higest weight module of level one as a module over a quantized classical universal enveloping algebra.

The finitistic dimension of a triangulated category is introduced. For the category of perfect complexes over a ring it is shown that this dimension is finite if and only if the small finitistic dimension of the ring is finite.

Let $A$ be a Nakayama algebra with $n$ simple modules and a simple module $S$ of even projective dimension $m$. Choose $m$ minimal such that a simple $A$-module with projective dimension $2m$ exists, then we show that the global dimension…

The fact that each finite-dimensional algebra over a field is isomorphic to the centralizer of two matrices, has suggested to investigate representation theoretical problems of finite-dimensional algebras through centralizer algebras of…

We study a generalization of Nagata idealization for level algebras. These algebras are standard graded Artinian algebras whose Macaulay dual generator is given explicity as a bigraded polynomial of bidegree $(1,d)$. We consider the algebra…

We explain the notion of colimit in category theory as a potential tool for describing structures and their communication, and the notion of higher dimensional algebra as a potential yoga for dealing with processes and processes of…

Determining the dimensions of nanostructures is critical to ensuring the maximum performance of many geometry-sensitive nanoscale functional devices. However, accurate metrology at the nanoscale is difficult using optics-based methods due…

We show that for pseudoeffective projective pairs the termination of one sequence of flips implies the termination of all flips, assuming a natural conjecture on the behaviour of the Nakayama-Zariski decomposition under the operations of a…

We classify Nichols algebras of irreducible Yetter-Drinfeld modules over nonabelian groups satisfying an inequality for the dimension of the homogeneous subspace of degree two. All such Nichols algebras are finite-dimensional, and all known…

In this paper, we construct derived equivalences between certain Nakayama algebras by using the notion of an S-family which is a family of objects in a triangulated category satisfying some axioms.

We give a complete classification of all $d$-representation-finite symmetric Nakayama algebras and of all $d$-representation-finite trivial extensions of path algebras of quivers, over an arbitrary field. As a consequence we get a…

In 2005, the second author and Todorov introduced an upper bound on the finitistic dimension of an Artin algebra, now known as the {\phi}-dimension. The {\phi}-dimension conjecture states that this upper bound is always finite, a fact that…