Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.16746

Superdecomposable Complete Path Algebras

Can Hatipoğlu·Christian Lomp
View original source ↗Read source document ↗Export metadata ↓

Abstract

Generalizing the setting of the second author's work on indecomposable modules without nonzero hollow factors, we characterize quivers $Q$ for which the dual algebra $R$ of the path coalgebra of $Q$, equivalently the complete path algebra, has no nonzero uniform right ideals: this happens exactly when every vertex of $Q$ can reach a vertex emitting at least two distinct arrows. Equivalently, the injective hull $E(R)$ of the right regular module is superdecomposable. These conditions are also equivalent to the path coalgebra having no nonzero hollow factor modules as a left module over its dual algebra.

Explore related subjects

math.RA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Can Hatipoğlu, Christian Lomp. 2026-10-12. Superdecomposable Complete Path Algebras. https://arxiv.org/abs/2610.16746

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Orthogonality of Defect Ideals for Jordan Homomorphisms

Let $φ\colon A\to B$ be a Jordan homomorphism of associative algebras over a field $\mathbb{F}$ of characteristic different from $2$, with defect ideals $V_φ$ and $W_φ$. If $A=\operatorname{Alg}([[A,A],[A,A]])$, then $V_φW_φ=W_φV_φ=0$ and $V_φ\cap W_φ\subseteq\operatorname{Ann}(\operatorname{Alg}(φ(A)))$. Moreover, the induced map modulo $V_φ\cap W_φ$ is standard. The annihilator bound is sharp, even in finite dimension. As an application, when $A$ is unital and $A=K(A)$, every Jordan homomorphism defined on $A$ is splittable and standard. In this setting, the corresponding result of Brešar and Zelmanov holds without the surjectivity hypothesis.

math.RA↗
arXiv2026

On the Real Waring Rank of a Biharmonic Form

We develop an effective method for determining the real Waring rank and the real border rank of biharmonic binary forms. By means of real apolarity, we convert both of these problems into membership questions for regions bounded by a hypocycloid and an epicycloid. We further provide a computable algebraic criterion for the relevant memberships, which involves only the signs of certain real-valued resultants.

math.RA↗
arXiv2026

Actions of central Morita monoidal groupoids, and seven term exact sequences of all types

We introduce a strict monoidal groupoid associated with a given commutative ring $K$. It acts on the Clifford extension systems of $K$-central algebras which are graded by a group $G$, as well as on the generalized collective characters, both of type $ϕ\in$ Hom$(G,$ Aut$(K))$. These actions partition the two sets above with respect to graded Morita equivalence. By that we establish a seven term exact sequence of type $ϕ$, which boils down to the celebrated Chase-Harrison-Rosenberg sequence when $ϕ$ is Galois.

math.RA↗