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

Author(s)

Pchelintsev, Sergey V. ^{[1, 2]} ; Shestakov, Ivan P. ^{[3, 4]}

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

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