On Solvability of Automorphism Groups of Commutative Algebras
Dibyendu Das

TL;DR
This paper investigates conditions under which the identity component of the automorphism group of a finite-dimensional commutative algebra is solvable, extending previous work by removing restrictions on the radical quotient dimension.
Contribution
It provides new sufficient conditions for the solvability of automorphism groups of commutative algebras, generalizing prior results that required specific radical quotient dimensions.
Findings
Established new criteria for solvability of automorphism groups
Extended previous results to broader classes of algebras
Removed restrictions on the dimension of the radical quotient
Abstract
Let be a finite-dimensional commutative associative algebra with unity over an algebraically closed field . The purpose of the paper is to study the solvability of , where is the identity component of . Inspired by Pollack's work, Saor\'in and Asensio have started this study for a commutative associative algebra when , where is the Jacobson radical of . In this paper, we give new sufficient conditions on so that is solvable without any restriction on .
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Taxonomy
TopicsAdvanced Topics in Algebra · Finite Group Theory Research · Algebraic structures and combinatorial models
