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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Author(s):
Pchelintsev, Sergey V. [1, 2] ; Shestakov, Ivan P. [3, 4]
Total Authors: 2
Affiliation:
[1] Finance Univ Govt Russian Federat, Moscow - Russia
[2] Moscow City Pedag Univ, Moscow - Russia
[3] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo - Brazil
[4] Sobolev Inst Math, Novosibirsk - Russia
Total Affiliations: 4
Document type: Journal article
Source: Journal of Algebra; v. 423, p. 54-86, FEB 1 2015.
Web of Science Citations: 11
Abstract

It is proved that the prime degenerate (-1, 1) algebra constructed in {[}12] (the (-1, 1)-monster) generates the same variety of algebras as the Grassmann (-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 {[}121]) 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. (C) 2014 Elsevier Inc. All rights reserved. (AU)

FAPESP's process: 12/04702-7 - Prime alternative and (-1,1)--algebras and superalgebras: subalgebras, ideals, C--operations, and identities
Grantee:Ivan Chestakov
Support type: Research Grants - Visiting Researcher Grant - International
FAPESP's process: 10/50347-9 - Algebras, representations e applications
Grantee:Ivan Chestakov
Support type: Research Projects - Thematic Grants