Related papers: The Igusa-Todorov $\phi$ function for truncated pa…

This article sets out to understand the categories $\QGr A$ where $A$ is either a monomial algebra or a path algebra of finite Gelfand-Kirillov dimension. The principle questions are: 1) What is the structure of the point modules up to…

Let A be a path A-infinity-algebra over a positively graded quiver Q. It is proved that the derived category of A is triangulated equivalent to the derived category of kQ, which is viewed as a dg algebra with trivial differential. The main…

We study the restricted form of the qaunatized enveloping algebra of an untwisted affine Lie algebra and prove a triangular decomposition for it. In proving the decomposition we prove several new identities in the quantized algebra, one of…

Working over a field $\kk$ of characteristic zero, this paper studies line embeddings of the form $\phi = (T_i,T_j,T_k):\A^1\to\A^3$, where $T_n$ denotes the degree $n$ Chebyshev polynomial of the first kind. In {\it Section 4}, it is shown…

Let ${\mathcal B}_{\mathfrak{q}}$ be a finite-dimensional Nichols algebra of diagonal type with braiding matrix $\mathfrak{q}$, let $\mathcal{L}_{\mathfrak{q}}$ be the corresponding Lusztig algebra as in arXiv:1501.04518 and let…

Let $C$ be a unital AH-algebra and let $A$ be a unital separable simple C*-algebra with tracial rank no more than one. Suppose that $\phi, \psi: C\to A$ are two unital monomorphisms. With some restriction on $C,$ we show that $\phi$ and…

The Gelfand-Kirillov dimension is a well established quantity to classify the growth of infinite dimensional algebras. In this article we introduce the algebraic entropy for path algebras. For the path algebras, Leavitt path algebras and…

A pathway from one vertex of a quiver to another is a reduced path. We modify the classical definition of quiver representations and we prove that semi-invariant polynomials for filtered quiver representations come from diagonal entries if…

In this paper, we consider the linearized translator equation $L_\phi u=f$, around entire convex translators $M=\textrm{graph}(\phi)\subset\mathbb{R}^4$, i.e. in the first dimension where the Bernstein property fails. Here, $L_\phi…

Tilings of a quadriculated annulus A are counted according to volume (in the formal variable q) and flux (in p). We consider algebraic properties of the resulting generating function Phi_A(p,q). For q = -1, the non-zero roots in p must be…

We consider autonomous conservative dynamical systems which are constrained with the condition that the total energy of the system has a specified value. We prove a theorem which provides the quadratic first integrals (QFIs), time-dependent…

Consider a sequence of integral matrices $\mathcal{A}=(A_n)_{n\in\N}$, and a $d$-tuple function ${\bf r}=(r_1,\ldots,r_d)\colon \N\to (0,\frac{1}{2})$. For a fixed vector ${\bm \alpha},$ we are interested in the set $\mathcal{T}_{{\bm…

Importance of theorem dedicated to isomorphisms consist in statement that they allow to identify different mathematical objects which have something common from the point of view of certain model. This paper considers morphisms of \Ts…

In this paper we study the representation dimension as well as the derived dimension of the path algebra of an artin algebra over a finite and acyclic quiver.

We examine situations, where representations of a finite-dimensional $F$-algebra $A$ defined over a separable extension field $K/F$, have a unique minimal field of definition. Here the base field $F$ is assumed to be a $C_1$-field. In…

For a real analytic periodic function $\phi:\mathbb{R}\to \mathbb{R}$, an integer $b\ge 2$ and $\lambda\in (1/b,1)$, we prove the following dichotomy for the Weierstrass-type function $W(x)=\sum\limits_{n\ge 0}{{\lambda}^n\phi(b^nx)}$:…

We construct an algebra of dimension $2^{\aleph_0}$ consisting only of functions which in no point possess a finite one-sided derivative. We further show that some well known nowhere differentiable functions generate algebras, which contain…

Recently there has been considerable interest in studying the length and the depth of finite groups, algebraic groups and Lie groups. In this paper we introduce and study similar notions for algebras. Let $k$ be a field and let $A$ be an…

Let $\phi$ be a birational map of the complex projective plane. We know that $\phi$ can be written as a composition of automorphisms of $\mathbb{P}^2_\mathbb{C}$ and the standard quadratic birational map $\sigma$. This writing, that is…

We obtain a remainder estimate for the truncated Taylor expansion for differential equations driven by weakly geometric $\Pi $-rough paths for $\Pi =\left( p_{1},\cdots ,p_{k}\right) $, $p_{i}\geq 1$. When there exists $ p\geq 1$ such that…