Jordan $*$-derivations of incidence algebras

Liuqing Yang

arXiv:2507.13751·math.RA·July 21, 2025

Jordan $*$-derivations of incidence algebras

Liuqing Yang

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TL;DR

This paper characterizes Jordan $*$-derivations of incidence algebras over locally finite posets, showing they are inner and transposed, and identifies the existence of Jordan $*$-derivations that are not $*$-derivations.

Contribution

It proves that all Jordan $*$-derivations are inner and transposed, and demonstrates the existence of Jordan $*$-derivations that are not $*$-derivations.

Findings

01

Every Jordan $*$-derivation is an inner $*$-derivation.

02

Every Jordan $*$-derivation is a transposed Jordan $*$-derivation.

03

Existence of Jordan $*$-derivations that are not $*$-derivations.

Abstract

Let $X$ be a locally finite partially ordered set (poset), $K$ a field of characteristic not 2, and $I (X, K)$ the incidence algebra over $K$ . In this paper, we prove that every Jordan $*$ -derivation of $I (X, K)$ is an inner $*$ -derivation and a transposed Jordan $*$ -derivation. Moreover, we demonstrate the existence of Jordan $*$ -derivations that are not $*$ -derivations.

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Taxonomy

TopicsAdvanced Topics in Algebra · Fuzzy and Soft Set Theory · Advanced Algebra and Logic