Advances in Applied Clifford Algebras

, Volume 27, Issue 2, pp 1917–1925 | Cite as

S3 Invariants of Finite Dimensional Real Division Algebras

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Abstract

Finite dimensional real division algebras are examined under the permutation of their structure constants. It is noted that there is only one finite-dimensional real flexible division algebras with an automorphism group isomorphic to S3. We show that the 8-dimensional real division algebras with derivation algebra g2 are isotopic under all permutations of the structure constants. Being a composition algebra is preserved under all permutations. We simultaneously derive information about the quaternion division algebras as subalgebras of the eight dimensional algebras. Finally, a division algebra with derivation algebra \({su(2)\oplus su(2)}\) is looked at under the actions of S3. The quaternion, octonion and Okubo algebras are special cases of our results.

Mathematics Subject Classification

Primary 05C38 15A15 Secondary 05A15 15A18 

Keywords

Division algebras Derivations Composition algebras Structure constants 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.The University of Texas at San Antonio, One UTSA CircleSan AntonioUSA

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