[math-fun] Gyroalgebra?

I was recently introduced to the notion of a "gyrovector" in the context of special relativity. Addition of velocities in the open ball G = {v s.t. ||v|| < c} is not associative, but there's a deformation of associativity that holds, namely a⊕(b⊕c) = (a⊕b)⊕gyr[a, b](c), where gyr[a, b] is an automorphism of the groupoid (G, ⊕). Does anyone know if there's a notion of "multiplication" of gyrovectors to get a "gyroalgebra"? I expect the multiplication wouldn't be associative, either. Googling "gyroalgebra" gives a single hit, and there it's used to mean calculating velocities with gyrovectors, not the multiplicative structure. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com