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Lye is a hydroxide, either sodium hydroxide or potassium hydroxide. The word lye most accurately refers to sodium hydroxide (NaOH), [ citation needed ] but historically has been conflated to include other alkali materials, most notably potassium hydroxide (KOH).
A blue lie is a form of lying that is told purportedly to benefit a collective or "in the name of the collective good". The origin of the term "blue lie" is possibly from cases where police officers made false statements to protect the police force, or to ensure the success of a legal case against an accused. [11]
The language of category theory provides a concise definition for Lie groups: a Lie group is a group object in the category of smooth manifolds. This is important, because it allows generalization of the notion of a Lie group to Lie supergroups.
A lie is a type of deception, an untruth or not telling the truth. Lie, LIE or A Lie may also refer to: Places ... Lye (disambiguation) The Lie (disambiguation)
The foundation of Lie theory is the exponential map relating Lie algebras to Lie groups which is called the Lie group–Lie algebra correspondence. The subject is part of differential geometry since Lie groups are differentiable manifolds. Lie groups evolve out of the identity (1) and the tangent vectors to one-parameter subgroups generate the ...
the real numbers, the Lie bracket is zero 1 R n: the Lie bracket is zero n: R 3: the Lie bracket is the cross product: Yes Yes 3: H: quaternions, with Lie bracket the commutator 4 Im(H) quaternions with zero real part, with Lie bracket the commutator; isomorphic to real 3-vectors, with Lie bracket the cross product; also isomorphic to su(2) and ...
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Lay and its principal derivatives (laid, laying) are correctly used in these examples: Now I lay me down to sleep. The chicken is laying an egg. Lie is an intransitive verb and cannot take an object. Lie and its principal derivatives (lay, lain, lying) are correctly used in these examples: My mother lies [not lays] down after meals.