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Full-Text Articles in Physical Sciences and Mathematics
Linear Mappings Satisfying Some Recursive Sequences, Amin Hosseini, Mehdi Mohammadzadeh Karizaki
Linear Mappings Satisfying Some Recursive Sequences, Amin Hosseini, Mehdi Mohammadzadeh Karizaki
Turkish Journal of Mathematics
Let $\mathcal{A}$ be a unital, complex normed $\ast$-algebra with the identity element $\textbf{e}$ such that the set of all algebraic elements of $\mathcal{A}$ is norm dense in the set of all self-adjoint elements of $\mathcal{A}$ and let $\{D_n\}_{n = 0}^{\infty}$ and $\{\Delta_n\}_{n = 0}^{\infty}$ be sequences of continuous linear mappings on $\mathcal{A}$ satisfying \[ \left\lbrace \begin{array}{c l} D_{n + 1}(p) = \sum_{k = 0}^{n}D_{n - k}(p)D_k(p),\\ \\ \Delta_{n + 1}(p) = \sum_{k = 0}^{n}\Delta_{n - k}(p)D_k(p), \end{array} \right. \] for all projections $p$ of $\mathcal{A}$ and all nonnegative integers $n$. Moreover, suppose that $D_0(p) = D_0(p)^2$ holds for all projections …
Dual Quaternion Algebra And Its Derivations, Eyüp Kizil, Yasemi̇n Alagöz
Dual Quaternion Algebra And Its Derivations, Eyüp Kizil, Yasemi̇n Alagöz
Turkish Journal of Mathematics
It is well known that the automorphism group $Aut(H)$ of the algebra of real quaternions $H$ consists entirely of inner automorphisms $i_{q}:p\rightarrow q\cdot p\cdot q^{-1}$ for invertible $q\in H$ and is isomorphic to the group of rotations $SO(3)$. Hence, $H$ has only inner derivations $D=ad(x),$ $x\in H$. See [4] for derivations of various types of quaternions over the reals. Unlike real quaternions, the algebra $H_{d}$ of dual quaternions has no nontrivial inner derivation. Inspired from almost inner derivations for Lie algebras, which were first introduced in [3] in their study of spectral geometry, we introduce coset invariant derivations for dual …