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arxiv: math/0611501 · v3 · submitted 2006-11-16 · 🧮 math.QA · math.RA

Varieties of dialgebras and conformal algebras

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keywords algebrasdialgebrasvarietyalgebraconformalembeddedeveryleibniz
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For a given variety Var of algebras we define the variety Var of dialgebras. This construction turns to be closely related with varieties of pseudo-algebras: every Var-dialgebra can be embedded into an appropriate pseudo-algebra of the variety Var. In particular, Leibniz algebras are exactly Lie dialgebras, and every Leibniz algebra can be embedded into current Lie conformal algebra.

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