TL;DR
This paper generalizes the Kantor Double construction to nonunital algebras, providing conditions for the resulting algebra to be Jordan and analyzing superderivations in prime cases.
Contribution
It introduces a generalized Kantor Double for nonunital algebras and characterizes when it is Jordan, also describing superderivations in prime cases.
Findings
Necessary and sufficient conditions for Jordan property
Description of $$-superderivations in prime cases
Extension of Kantor Double to nonunital algebras
Abstract
We consider generalization of wellknown construction Kantor Double J({\Gamma}, {,}) (KKM Double, Kantor-King-McCrimmon Double), where basic algebra {\Gamma} is nonunital algebra. We find necessary and sufficient conditions for a generalized Kantor double to be Jordan. We also describe -superderivations of a generalized Kantor double whose even part is prime.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons