Nil algebras with restricted growth
T H Lenagan, Agata Smoktunowicz, Alexander Young
TL;DR
This paper constructs a finitely generated algebra over any countable field that is nil, infinite-dimensional, and has controlled growth, specifically with Gelfand-Kirillov dimension at most three.
Contribution
It demonstrates the existence of such algebras with restricted growth and nil properties, expanding understanding of algebraic structures with specific dimensional constraints.
Findings
Existence of finitely generated nil algebras over countable fields
Construction of infinite-dimensional algebras with Gelfand-Kirillov dimension ≤ 3
Algebras exhibit controlled growth and nilpotency
Abstract
It is shown that over an arbitrary countable field, there exists a finitely generated algebra that is nil, infinite dimensional, and has Gelfand-Kirillov dimension at most three.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topics in Algebra · Advanced Algebra and Logic