Classification of 4-dimensional associative algebras with principal generators over complex numbers

Journal of Hebei University of Science and Technology

Haiyang LI¹  Changzhou LI¹ 

[1] School of Science, Xi'an Polytechnic University, Xi'an, Shaanxi 710048, China;

关键词: ring theory;    associative algebras;    quotient algebras;    4-dimensional associative algebras with principal generators;    isomorphism classification;   

DOI  :  10.7535/hbkd.2017yx02002

来源: DOAJ

【 摘 要 】

In order to obtain the classification of 4-dimensional associative algebras with principal generators over complex number C under isostructuralism, by using the ring theory and distribution of roots of the equations satisfied by the principal generators: one quadruple root, four different roots, one triple root and one simple root, two different double roots, one double root and two different simple roots, the above equations are translated and stretched, then the more simple equations are obtained. By using linear algebras, quotient algebras and maple to make a large number of operations, it is concluded that each isomorphism type has nothing to do with parameters. Finally by comparing each isomorphism type, the complete classification is obtained, which deepens the realization of structure of asso ciative algebra, and provides reference for relative study.

【 授权许可】

Unknown