NDLI: Some Identities in Algebras Obtained by the Cayley-Dickson Process

Content Provider	Springer Nature Link
Author	Flaut, Cristina Shpakivskyi, Vitalii
Copyright Year	2012
Abstract	Polynomial identities in algebras are the central objects of Polynomial Identities Theory. They play an important role in learning of algebras properties. In particular, the Hall identity is fulfilled in the quaternion algebra and does not hold in other non-commutative associative algebras. For this reason, the Hall identity is important for the quaternion algebra. The idea of this work is to generalize the Hall identity to algebras obtained by the Cayley-Dickson process.Starting from the above remarks, in this paper, we prove that the Hall identity is true in all algebras obtained by the Cayley-Dickson process and, in some conditions, the converse of this statement is also true for split quaternion algebras. From Hall identity, we will find some new properties and identities in algebras obtained by the Cayley-Dickson process.
Starting Page	63
Ending Page	76
Page Count	14
File Format	PDF
ISSN	01887009
Journal	Advances in Applied Clifford Algebras
Volume Number	23
Issue Number	1
e-ISSN	16614909
Language	English
Publisher	SP Birkhäuser Verlag Basel
Publisher Date	2012-06-29
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Cayley-Dickson process Clifford algebras Hall identity Mathematical Methods in Physics Theoretical, Mathematical and Computational Physics Applications of Mathematics Physics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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Some Identities in Algebras Obtained by the Cayley-Dickson Process