Classification of Associative Algebras Satisfying Quadratic Polynomial Identities |Chapter 5 | Mathematics and Computer Science: Research Updates Vol. 8

 

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 X2 = 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 X2 = 0 over fields of characteristics different from 2 are nilpotent of index 3.

 

 

Author(s) Details

Josimar da Silva Rocha
Department of Mathematics, Universidade Tecnol´ogica Federal do Paran´a, Corn´elio Proc´opio Campus, Corn´elio Proc´opio, Paran´a, Brazil.

 

Please see the book here :- https://doi.org/10.9734/bpi/mcsru/v8/6615