
TL;DR
This paper explores conditions under which extensions of nilpotent Lie algebras and Loday algebras remain nilpotent, establishing analogues and implications for associative and diassociative algebra structures.
Contribution
It proves new results on the nilpotency of algebra extensions, extending known Lie algebra results to Loday and diassociative algebras.
Findings
Nilpotency of extensions depends on lifts of a map to Out(A)
Analogues of Lie algebra results are established for Loday algebras
Associative algebra case is derived as a special instance
Abstract
Given a pair of nilpotent Lie algebras and , an extension is not necessarily nilpotent. However, if and are extensions which correspond to lifts of a map , it has been shown that is nilpotent if and only if is nilpotent. In the present paper, we prove analogues of this result for the algebras of Loday. As an important consequence, we thereby gain its associative analogue as a special case of diassociative algebras.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology
