Abstract
We study a series of real nonassociative algebras π p, q introduced in [Citation5]. These algebras have a natural -grading, where n = p + q, and they are characterized by a cubic form over the field β€2. We establish all the possible isomorphisms between the algebras π p, q preserving the structure of -graded algebra. The classification table of π p, q is quite similar to that of the real Clifford algebras Cl p, q , the main difference is that the algebras π n, 0 and π0, n are exceptional.
ACKNOWLEDGMENTS
The authors are grateful to Valentin Ovsienko for enlightening discussions.
Notes
Communicated by A. Elduque.
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