Authors: Bijan Kumar Patel ; Prasanta Kumar Ray

The aim of this article is to investigate two new classes of quaternions, namely, balancing and Lucas-balancing quaternions that are based on balancing and Lucas-balancing numbers, respectively. Further, some identities including Binet’s formulas, summation formulas, Catalan’s identity, etc. concerning these quaternions are also established.

• 11B39 - Fibonacci and Lucas numbers and polynomials and generalizations
• 20G20 - Linear algebraic groups over the reals, the complexes, the quaternions