Abstract
The aim of this paper is to describe the irreducible modules for the Jordan algebra of 2 × 2 matrices over an algebraically closed field of characteristic different from 2, 3 and 5 in the class of the commutative power-associative algebras. All irreducible non-unital modules, and irreducible unital modules up to dimension three are classified, namely we find seven non-parameterized and five families of parameterized modules of dimension three. For every , an irreducible module of dimension 3k is also constructed.
2020 MATHEMATICS SUBJECT CLASSIFICATION:
Acknowledgments
The authors would like to thank the anonymous referee for his/her helpful comments that improved the quality of the manuscript. E. Quintero Vanegas would like to thank the Universidade Federal da Bahia (UFBA) where part of the results were obtained.