In this paper, we study the derivations of a train algebra of degree 2 and exponent 3. We give a characterization of these derivations using a Peirce decomposition. A more detailed description is made for the case of dimension 3. For automorphisms, the study is made for the type (1 + r, s, 0).

derivations, train algebra, Peirce decomposition.

Received: November 9, 2022; Accepted: January 16, 2023; Published: February 4, 2023

How to cite this article: André Conseibo, Derivations and automorphisms of train algebra of degree 2 and exponent 3, Universal Journal of Mathematics and Mathematical Sciences 18(2) (2023), 145-164. http://dx.doi.org/10.17654/2277141723009

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] M. T. Alcalde, C. Burgueño, A. Labra and A. Micali, Sur les algèbres de Bernstein, Proc. London Math. Soc. (3) 58(1) (1989), 51-68 (in French).
[2] M. T. Alcalde, C. Burgueño and C. Mallol, Dérivations dans les algèbres de Bernstein, J. Algebra 183 (1996), 826-836.
[3] I. Basso, R. Costa, J. Carlos Gutiérrez and H. Guzzo, Jr., Cubic algebras of exponent 2: basic properties, Int. J. Math. Game Theory and Algebra 9(4) (1999), 245-258.
[4] J. Bayara, A. Conseibo, M. Ouattara and A. Micali, Train algebras of degree 2 and exponent 3, Discrete Contin. Dyn. Syst. Ser. S 4(6) (2011), 1371-1386.
[5] H. Guzzo, Jr., The Peirce decomposition for commutative train algebras, Comm. Algebra 22 (1994), 5745-5757.
[6] A. Micali and M. Ouattara, Structure des algèbres de Bernstein, Linear Algebra Appl. 218 (1995), 77-88.
[7] R. D. Schafer, An Introduction to Nonassociative Algebras, Academic Press, New York, 1966.
[8] A. Wörz-Busekros, Algebras in genetics, Lecture Notes in Biomathematics, 36, Springer-Verlag, Berlin-New York, 1980.