In
algebra
Algebra () is one of the areas of mathematics, broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathem ...
, a Lie-admissible algebra, introduced by , is a (possibly
non-associative)
algebra
Algebra () is one of the areas of mathematics, broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathem ...
that becomes a
Lie algebra
In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi iden ...
under the bracket
'a'', ''b''= ''ab'' − ''ba''. Examples include
associative algebras,
Lie algebras, and
Okubo algebras.
See also
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Malcev-admissible algebra
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Jordan-admissible algebra In algebra, a noncommutative Jordan algebra is an algebra, usually over a field of characteristic not 2, such that the four operations of left and right multiplication by ''x'' and ''x''2 all commute with each other. Examples include associative al ...
References
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{{Authority control
Non-associative algebra