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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Noncommutative matrix Jordan algebras


Authors: Robert B. Brown and Nora C. Hopkins
Journal: Trans. Amer. Math. Soc. 333 (1992), 137-155
MSC: Primary 17A15; Secondary 17A36, 17B60
DOI: https://doi.org/10.1090/S0002-9947-1992-1068925-4
MathSciNet review: 1068925
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Abstract: We consider noncommutative degree two Jordan algebras $ \mathcal{J}$ of two by two matrices whose off diagonal entries are from an anticommutative algebra $ \mathcal{S}$ . We give generators and relations for the automorphism group of $ \mathcal{J}$ and determine the derivation algebra Der $ \mathcal{J}$ in terms of mappings on $ \mathcal{S}$ . We also give an explicit construction of all $ \mathcal{S}$ for which Der $ \mathcal{J}$ does not kill the diagonal idempotents and give conditions for nonisomorphic $ \mathcal{S}$ 's to give isomorphic $ \mathcal{J}$ 's.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1068925-4
Keywords: Degree two noncommutative Jordan algebra, derivation algebra, automorphism group, isomorphism
Article copyright: © Copyright 1992 American Mathematical Society