Right Alternative Superalgebras of Capacity 1 with Strongly Alternative Even Part
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DOI: 10.1007/s10469-020-09591-y
Abstract: We look at the structure of a unital right alternative superalgebra of capacity 1 over an algebraically closed field assuming that its even part is finite-dimensional and strongly alternative. It is proved that the condition… read more here.
Keywords: right alternative; part; capacity; even part ... See more keywords
The algebraic and geometric classification of nilpotent right alternative algebras
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DOI: 10.1007/s10998-021-00386-x
Abstract: We present algebraic and geometric classifications of the 4-dimensional complex nilpotent right alternative algebras. Specifically, we find that, up to isomorphism, there are only 9 non-isomorphic nontrivial nilpotent right alternative algebras. The corresponding geometric variety… read more here.
Keywords: right alternative; algebraic geometric; nilpotent right; alternative algebras ... See more keywords
Right alternative bimodules over Cayley algebra and coordinatization theorem
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DOI: 10.1016/j.jalgebra.2020.12.009
Abstract: Abstract It is proved that every unital right alternative bimodule over a Cayley algebra (over an algebraically closed field of characteristic not 2) is alternative. Using this result, a coordinatization theorem is proved for unital… read more here.
Keywords: right alternative; alternative bimodules; cayley algebra; coordinatization theorem ... See more keywords