We introduce an interesting and instructive approach to the classification problem of two dimensional associative algebras over any field. We then complete their deformation theory and give some information to an open question in the algebraic deformation theory.

classification of associative algebras, algebraic deformation theory, rigidity, integrability.

Received: January 2, 2022; Accepted:January 20, 2022; Published: March 3, 2022

How to cite this article: Murray Gerstenhaber and Fujio Kubo, On the deformation of the two dimensional associative algebras, JP Journal of Algebra, Number Theory and Applications 54 (2022), 1-17. http://dx.doi.org/10.17654/0972555522012

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