Abstract
Derivations of generalized quaternion algebra
Highlights
Derivations of an algebra give interesting insights for studying its algebraic structure
Derivations of Lie algebras have been used in a control theoretical setting since they are intimately related with linear vector fields
By a linear vector field on a Lie group G we mean that its flow forms a 1-parameter subgroup of the group of G -automorphisms
Summary
Derivations of an algebra give interesting insights for studying its algebraic structure. We first state the conditions that a linear map should obey to become a derivation for the generalized quaternion algebra under consideration and we obtain a typical derivation in its matrix form. We constrain ourselves only to the task of determining generalized derivations of quaternion algebra in the matrix form.
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