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Some Results On Quaternion 3-Space
Abstract
In this paper, the set J′=H(Q₄,Jγ) of 4 by 4 matrices, with
entries in a quaternion F-algebra Q, that are symmetric with respect to the
canonical involution Jγ is studied. J′
is also the special Jordan matrix algebra and some results related to points
and lines of the quaternion 3-space P(J′)
defined by the algebra are introduced. Finally, by taking dual ring Q:= Q+Qε (ε∉Q, ε²=0) instead of Q,
the obtained results are carried to a more general state.
Keywords
References
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- [4]. Celik, B. and Dayioglu, A., The Collineations which Act as Addition and Multiplication on Points in a Certain Class of Projective Klingenberg Planes, Journal of Inequalities and Applications, 193 (2013).
- [5]. Faulkner, J.R., Octonion Planes Defined by Quadratic Jordan Algebras, Mem. Amer. Math. Soc., 104 (1970) 1-71.
- [6]. Faulkner, J.R., The Role of Nonassociative Algebra in Projective Geometry, Graduate Studies in Mathematics, Vol. 159, Amer. Math. Soc., Providence, R.I., (2014).
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Details
Primary Language
English
Subjects
-
Journal Section
Research Article
Publication Date
June 29, 2018
Submission Date
April 10, 2017
Acceptance Date
April 10, 2018
Published in Issue
Year 2018 Volume: 39 Number: 2