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Mathematics > Rings and Algebras

arXiv:1311.7587 (math)
[Submitted on 29 Nov 2013]

Title:Prime (-1,1) and Jordan monsters and superalgebras of vector type

Authors:Sergey V. Pchelintsev, Ivan P. Shestakov
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Abstract:It is proved that the prime degenerate (-1,1) algebra constructed in [13] (the (-1,1)-monster) generates the same variety of algebras as the Grassman (-1,1)-algebra. Moreover, the same variety is generated by the Grassmann envelope of any simple nonassociative (-1,1)-superalgebra. The variety occurs to be the smallest variety of (-1,1)-algebras that contains prime nonassociative algebras. Similar results are obtained for Jordan algebras. Thus, the Jordan monster (the prime degenerate algebra constructed in [13]) and the Grassmann envelope of the prime Jordan superalgebra of vector type have the same ideals of identities. It is also shown that the Jordan monster generates a minimal variety that contains prime degenerate Jordan algebras. All the algebras and superalgebras are considered over a field of characteristic 0.
Subjects: Rings and Algebras (math.RA)
MSC classes: 17A70, 17D25
Cite as: arXiv:1311.7587 [math.RA]
  (or arXiv:1311.7587v1 [math.RA] for this version)
  https://doi.org/10.48550/arXiv.1311.7587

Submission history

From: Ivan Shestakov [view email]
[v1] Fri, 29 Nov 2013 14:59:58 UTC (25 KB)
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