Work

Affine Nilpotency and Engel's Theorem for Lie Affgebras

Year: 2026

Type: preprint

Abstract: We study some structural properties of Lie affgebras as affine analogues of Lie algebras. We introduce the notion of an ideaf, the affine counterpart of an ideal, and establish characterizations of left and right ideafs. We further study centers, quotient structures, and product ideafs, proving, under suitable conditions, that the center of a Lie affgebra is an ideaf. We then develop the notion of affine nilpotency and establish connections between the nilpotency of Lie affgebras and that of their retracted Lie algebras. As an application, we prove an Engel-type theorem for Lie affgebras of the form $\mathfrak{a}(\mathfrak{g};κ=2λ,λ,s)$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.15190

Authors: Anowar, Tarik, Saha, Ripan, Thokdar, Sayan

Institutions: Raiganj University, Indian Institute of Science Education and Research Pune

Topic: Advanced Topics in Algebra

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Arthritis National Research Foundation, National Research Foundation, Department of Science and Technology, Ministry of Science and Technology, India, Science and Engineering Research Board

Award: G3737107500

OpenAlex ID: W7203672765

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