Malaysian Journal of Mathematical Sciences, March 2023, Vol. 17, No. 1

Genetic Algebras generated by $b-$bistochastic Quadratic Stochastic Operators: The Character and Associativity

Embong, A. F., Zulkifly. M. I. E., and Awg Arifin, D. N. A.

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Received date: 20 April 2021
Accepted date: 1 February 2023

In the present paper we consider a genetic algebra induced by $ b- $bistochastic Quadratic Stochastic Operators (QSOs) which is called $ b- $bistochastic genetic algebra. First, we characterize their nontrivial character function on $ \mathbb{R}^{n} $. It turns out that, the given character function is not unique, hence full descriptions of such functions on $ \mathbb{R}^{1} $ and $ \mathbb{R}^{2} $ are established. Moreover, the defined algebra is commutative but not associative in general, hence, the associativity of $ b- $bistochastic genetic algebras defined on $ \mathbb{R}^{1} $ and $ \mathbb{R}^{2} $ are described. In this work, the existence of non-trivial derivations on such algebras are given.

Keywords: non-associative algebra; genetic algebra; b-bistochastic; quadratic stochastic operators; non-linear operator



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