Classification of Associative Algebras Satisfying Quadratic Polynomial Identities
Rings and Algebras
2025-12-09 v1
Abstract
In quantum mechanics, associative algebras play an important role in understanding symmetries and operator algebras, providing new algebraic frameworks for describing physical systems. This work classifies associative algebras over a field K that are generated by a finite set G and satisfy a polynomial identity of the form X^{2} = aX+b, where a and b are elements of K and X varies either over all elements of the algebra or over all elements of the multiplicative semigroup S generated by G. One of the results obtained in this work shows that algebras satisfying X^{2}=0 over fields of characteristics different from 2 are nilpotent of index 3. The results were computationally validated using the GAP system.
Keywords
Cite
@article{arxiv.2512.06125,
title = {Classification of Associative Algebras Satisfying Quadratic Polynomial Identities},
author = {Josimar da Silva Rocha},
journal= {arXiv preprint arXiv:2512.06125},
year = {2025}
}