Advances in Applied Clifford Algebras

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

S 3 Invariants of Finite Dimensional Real Division Algebras

  • G. P. Wene


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 S 3. We show that the 8-dimensional real division algebras with derivation algebra g 2 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 S 3. The quaternion, octonion and Okubo algebras are special cases of our results.

Mathematics Subject Classification

Primary 05C38 15A15 Secondary 05A15 15A18 


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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