The Cartan product is a generalization of the symmetric product of two vectors. We review its definition, present some examples, and exhibit its rôle in the construction of various natural algebras.
"The Cartan Product." Bull. Belg. Math. Soc. Simon Stevin 11 (5) 641 - 651, March 2005. https://doi.org/10.36045/bbms/1110205624