Algebras
_____________________________________________________________________________________________________
PERSONAL RESEARCH
_____________________________________________________________________________________________________
D. H. Delphenich, "The representation of physical motions by various types of quaternions," arXiv:1205.4440.
_____________________________________________________________________________________________________
TRANSLATIONS
_____________________________________________________________________________________________________
E. Study, "On systems of complex numbers and their application to the theory of transformation groups," Monatsber. f. Math. u. Phys. 1 (1890), 283-354.
G. Combebiac, "Calculus of tri-quaternions," Gauthier-Villars, Paris, 1902.
G. Frobenius, “Theory of hypercomplex quantities, I” Sitz. Kön. Preuss. Akad. Wiss. (1903), 504-537; Gesammelte Abhandlungen, art. 70, 284-317.
G. Frobenius, "Theory of hypercomplex numbers, II," Sitz. Kon. Preuss. Akad. Wiss. (1903), 634-645.
E. v. Weber, "Complex motions," Ber. sachs. Ges. der Wiss (1903), 384-408.
J. Grunwald, "On dual numbers and their application in geometry," Monatsh. f. Math. u. Phys. 17 (1906), 81-136.
E. Cartan, "The principle of duality and the theory of simple and semi-simple groups," Bull. des Sciences math. 49 (1925), 361-374.
J. A. Schouten, "On the hypercomplex numbers that are employed in the wave equation," Proc. Kon. Akad. Wet. Amst. 32 (1929), 105-108.
E. Noether, "The relationship of hypercomplex numbers systems to commutative algebra and number theory," Verhandl. Int. Math. Kongress Zurich 1 (1932), 189-194.
A. Einstein and W. Mayer, "Semi-vectors and spinors," Proc. Roy. Acad. Amst. 36 (1933), 522-550.
W. Scherrer, "Quaternions and Semi-vectors," Comm. Math. Helv. 7 (1935), 141-149.
J. Blaton, “Quaternions, semi-vectors, and spinors,” Zeit. Phys. 95 (1935), 337-354.
B. L. van der Waerden, Groups of Linear Transformations, Springer, Berlin, 1935; reprinted by Chelsea, N. Y., 1948.
M. Markic, "Transformants: A new mathematical vehicle. A synthesis of Combebiac's tri-quaternions and Grassmann's geometric system. The calculus of quadri-quaternions," Ann. fac. sci. Toulouse (3) 28 (1936), 103-148.
W. Blaschke, “Applications of dual quaternions to kinematics,” Annales Academiae Scientiarum Fennicae, (1958), 1-13; Gesammelte Werke, v. 2.
W. Blaschke, "Kinematics and quaternions," VEB, Deutscher Verlag der Wissenschaften, Berlin, 1960.
_______________________________________________________________________________________________________________________________________________________
_____________________________________________________________________________________________________
PERSONAL RESEARCH
_____________________________________________________________________________________________________
D. H. Delphenich, "The representation of physical motions by various types of quaternions," arXiv:1205.4440.
_____________________________________________________________________________________________________
TRANSLATIONS
_____________________________________________________________________________________________________
E. Study, "On systems of complex numbers and their application to the theory of transformation groups," Monatsber. f. Math. u. Phys. 1 (1890), 283-354.
G. Combebiac, "Calculus of tri-quaternions," Gauthier-Villars, Paris, 1902.
G. Frobenius, “Theory of hypercomplex quantities, I” Sitz. Kön. Preuss. Akad. Wiss. (1903), 504-537; Gesammelte Abhandlungen, art. 70, 284-317.
G. Frobenius, "Theory of hypercomplex numbers, II," Sitz. Kon. Preuss. Akad. Wiss. (1903), 634-645.
E. v. Weber, "Complex motions," Ber. sachs. Ges. der Wiss (1903), 384-408.
J. Grunwald, "On dual numbers and their application in geometry," Monatsh. f. Math. u. Phys. 17 (1906), 81-136.
E. Cartan, "The principle of duality and the theory of simple and semi-simple groups," Bull. des Sciences math. 49 (1925), 361-374.
J. A. Schouten, "On the hypercomplex numbers that are employed in the wave equation," Proc. Kon. Akad. Wet. Amst. 32 (1929), 105-108.
E. Noether, "The relationship of hypercomplex numbers systems to commutative algebra and number theory," Verhandl. Int. Math. Kongress Zurich 1 (1932), 189-194.
A. Einstein and W. Mayer, "Semi-vectors and spinors," Proc. Roy. Acad. Amst. 36 (1933), 522-550.
W. Scherrer, "Quaternions and Semi-vectors," Comm. Math. Helv. 7 (1935), 141-149.
J. Blaton, “Quaternions, semi-vectors, and spinors,” Zeit. Phys. 95 (1935), 337-354.
B. L. van der Waerden, Groups of Linear Transformations, Springer, Berlin, 1935; reprinted by Chelsea, N. Y., 1948.
M. Markic, "Transformants: A new mathematical vehicle. A synthesis of Combebiac's tri-quaternions and Grassmann's geometric system. The calculus of quadri-quaternions," Ann. fac. sci. Toulouse (3) 28 (1936), 103-148.
W. Blaschke, “Applications of dual quaternions to kinematics,” Annales Academiae Scientiarum Fennicae, (1958), 1-13; Gesammelte Werke, v. 2.
W. Blaschke, "Kinematics and quaternions," VEB, Deutscher Verlag der Wissenschaften, Berlin, 1960.
_______________________________________________________________________________________________________________________________________________________