相关论文: A uniqueness property of {\tau} exceptional sequen…
Many $W$-algebras (e.g. the $W_N$ algebras) are consistent for all values of the central charge except for a discrete set of exceptional values. We show that such algebras can be contracted to new consistent degenerate algebras at these…
We prove that a sequence satisfying a certain symmetry property is $2$-regular in the sense of Allouche and Shallit, i.e., the $\mathbb{Z}$-module generated by its $2$-kernel is finitely generated. We apply this theorem to develop a general…
We show that there is a special bijection between the indecomposable summands of the two modules which form a basic support $\tau$--tilting pair and the indecomposable summands of the two modules which form another basic support…
Happel and Unger reconstructed hereditary algebras from their posets of tilting modules. Inspired by this result, we try removing the assumption to be hereditary. However, it would be unfortunately fail in general: e.g. every selfinjective…
We show that in the hierarchical tile assembly model, if there is a producible assembly that overlaps a nontrivial translation of itself consistently (i.e., the pattern of tile types in the overlap region is identical in both translations),…
An algebra is said to be \emph{$\tau$-tilting finite} provided it has only a finite number of $\tau$-rigid objects up to isomorphism. We associate a category to each such algebra. The objects are the wide subcategories of its category of…
Inspired by tau-tilting theory [AIR], we introduce the notion of nu-stable support tau-tilting modules. For any finite dimensional selfinjective algebra {\Lambda}, we give bijections between two-term tilting complexes in Kb(proj {\Lambda}),…
We use the combinatorial properties of central sets to prove a result about the existence of exponential monochromatic patterns, in the style of Hindman's Finite Sums Theorem. More precisely, we prove that for every finite coloring of the…
The theory of $\tau$-tilting was introduced by Adachi--Iyama--Reiten; one of the main results is a bijection between support $\tau$-tilting modules and torsion classes. We are able to generalise this result in the context of the higher…
We show that any accordion complex associated to a dissection of a convex polygon is isomorphic to the support $\tau$-tilting simplicial complex of an explicit finite dimensional algebra. To this end, we prove a property of some induced…
We study the topological triviality and the Whitney equisingularity of a family of isolated determinantal singularities. On one hand, we give a L\^e-Ramanujam type theorem for this kind of singularities by using the vanishing Euler…
Trinh and Xue have proposed a startling conjecture on intersections of blocks of cyclotomic Hecke algebras occurring in modular representation theory of finite reductive groups. We prove this conjecture for all exceptional type groups apart…
For a tree $T$, let $i_T(t)$ be the number of independent sets of size $t$ in $T$. It is an open question, raised by Alavi, Malde, Schwenk and Erd\H{o}s, whether the sequence $(i_T(t))_{t \geq 0}$ is always unimodal. Here we answer the…
We discuss the problem of unitarity for Yang-Mills theory in the Landau gauge with a mass term a la Stueckelberg. We assume that the theory (non-renormalizable) makes sense in some subtraction scheme (in particular the Slavnov-Taylor…
We show any matrix of rank $r$ over $\mathbb{F}_q$ can have $\leq \binom{r}{k}(q-1)^k$ distinct columns of weight $k$ if $ k \leq O_q(\sqrt{\log r})$ (up to divisibility issues), and $\leq \binom{r}{k}(q-1)^{r-k}$ distinct columns of…
As a corollary to the recent extraordinary theorem of Maynard and Tao, we re-prove, in a stronger form, a result of Shiu concerning "strings" of consecutive, congruent primes.
We give a characterization of $\tau$-rigid modules over Auslander algebras in terms of projective dimension of modules. Moreover, we show that for an Auslander algebra $\Lambda$ admitting finite number of non-isomorphic basic tilting…
A complete first order theory of a relational signature is called monomorphic iff all its models are monomorphic (i.e. have all the $n$-element substructures isomorphic, for each positive integer $n$). We show that a complete theory…
H. Miyachi and W. Turner have independently proved that Broue's Abelian Defect Group Conjecture holds for certain unipotent blocks of the finite general linear group, the so-called Rouquier blocks. This together with A. Marcus and J. Chuang…
We give an example of a finite-dimensional algebra with a 2-cluster tilting module and a simple module which has infinite complexity. This answers a question of Erdmann and Holm.