JP Journal of Algebra, Number Theory and Applications

The JP Journal of Algebra, Number Theory and Applications is a prestigious international journal indexed in the Emerging Sources Citation Index (ESCI). It publishes original research papers, both theoretical and applied in nature, in various branches of algebra and number theory. The journal also welcomes survey articles that contribute to the advancement of these fields.

Submit Article

ON THE DEFORMATION OF THE TWO DIMENSIONAL ASSOCIATIVE ALGEBRAS

Authors

  • Murray Gerstenhaber
  • Fujio Kubo

Keywords:

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

DOI:

https://doi.org/10.17654/0972555522012

Abstract

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.

Received: January 2, 2022
Accepted: January 20, 2022

References

J. M. A. Bermúdez, J. Fresán and J. S. Hernández, On the variety of two dimensional real associative algebras, Int. J. Contemp. Math. Sci. 2 (2007), 1293-1305.

A. Cayley, On double algebra, Proc. Lond. Math. Soc. 15 (1883/84), 185-197.

P. Gabriel, Finite representation type is open, Lecture Notes in Math. 488 (1975), 132-155.

M. Gerstenhaber, On the deformation of rings and algebras, Ann. of Math. 79 (1964), 267-288.

M. Gerstenhaber and S. D. Schack, Relative Hochschild cohomology, rigid algebras, and the Bockstein, J. Pure Appl. Algebra 43 (1986), 53-74.

M. Gerstenhaber and S. D. Schack, Algebraic cohomology and deformation theory, Deformation Theory of Algebras and Structures and Applications, M. Hazewinkel and M. Gerstenhaber, eds., Kluwer Academic Publishers, Dordrecht, 1988.

G. Mazzola, The algebraic and geometric classification of associative algebras of dimension five, Manuscripta Math. 27 (1979), 81-101.

B. Pierce, Linear associative algebra, Amer. J. Math. 4 (1881), 97-229.

E. Study, Über Systeme complexer Zahlen und ihre Anwendung in der Theorie der Transformationsgruppen, Monatsh. Math. Phys. 1 (1890), 283-354 (in German).

Published

2022-03-03

Issue

Section

Articles

How to Cite

ON THE DEFORMATION OF THE TWO DIMENSIONAL ASSOCIATIVE ALGEBRAS. (2022). JP Journal of Algebra, Number Theory and Applications, 54, 1-17. https://doi.org/10.17654/0972555522012

Similar Articles

11-20 of 55

You may also start an advanced similarity search for this article.