The moment map for the variety of associative algebras
Hui Zhang, Zaili Yan

TL;DR
This paper studies the moment map for associative algebras, characterizing critical points, maxima, minima, and classifying these points for low-dimensional cases, revealing algebraic structures associated with these critical points.
Contribution
It provides a complete characterization of critical points of the moment map functional on associative algebras and classifies them for dimensions two and three, introducing new structural insights.
Findings
Critical points characterized by specific algebraic conditions.
Existence and uniqueness of Nikolayevsky derivation for each algebra.
Complete classification of critical points for dimensions 2 and 3.
Abstract
We consider the moment map for the action of on , and study the critical points of the functional . Firstly, we prove that is a critical point if and only if for some and where . Then we show that any algebra admits a Nikolayevsky derivation which is unique up to automorphism, and if moreover, is a critical point of , then Secondly, we characterize the maxima and minima of the functional , where denotes the projectivization of the…
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Algebra and Geometry
