On classification of 3-D rock-paper-scissor algebra

Abstract

This research was sought to define the three-dimension genetic and evolution algebras generated by non-ergodic quadratic stochastic operator, where these algebras were known as the Rock-Paper-Scissor algebras (RPS). These algebras were classified in terms of the parameters in the non-ergodic quadratic stochastic operator. We investigated the necessary and sufficient conditions when two three-dimension Rock-Paper-Scissor genetic and evolution algebras will be isomorphic. Moreover, we studied the cases of nilpotency and solvability of these algebras. Also, we studied the space of derivations of such algebras. In the end, all previous investigations (isomorphism, derivations, solvability, and nilpotency) were generalized for direct sum of such algebras.