The set of quaternions was introduced by Hamilton in 1843. In 2016, Özdemir introduced a generalization of quaternions, elliptic quaternions. In this paper, we introduce and study balancing elliptic quaternions, i.e. elliptic quaternions with balancing and Lucas-balancing coefficients. We give some of their properties, among others the Binet-type formula, the generating function, and the matrix representation of these quaternions.
Bród et al. (2026) studied this question.