From Rota–Baxter algebras to pre-Lie algebras
نویسندگان
چکیده
منابع مشابه
Free pre-Lie algebras are free as Lie algebras
We prove that free pre-Lie algebras, when considered as Lie algebras, are free. Working in the category of S-modules, we define a natural filtration on the space of generators. We also relate the symmetric group action on generators with the structure of the anticyclic PreLie operad.
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On the level of Lie algebras, the Kontsevich integral of a knot (a graph-valued invariant) becomes the colored Jones function (a power series invariant). Rozansky conjectured and the authors proved a Rationality Conjecture for the Kontsevich integral. In this note, we explain how the Rationality Conjecture is related to Lie groups.
متن کاملBeads: from Lie Algebras to Lie Groups
The Kontsevich integral of a knot is a powerful invariant which takes values in an algebra of trivalent graphs with legs. Given a Lie algebra, the Kontsevich integral determines an invariant of knots (the so-called colored Jones function) with values in the symmetric algebra of the Lie algebra. Recently A. Kricker and the author constructed a rational form of the Kontsevich integral which takes...
متن کاملBeads: from Lie Algebras to Lie Groups
The Kontsevich integral of a knot is a powerful invariant which takes values in an algebra of trivalent graphs with legs. Given a Lie algebra, the Kontsevich integral determines an invariant of knots (the so-called colored Jones function) with values in the symmetric algebra of the Lie algebra. Recently A. Kricker and the author constructed a rational form of the Kontsevich integral which takes...
متن کاملConstructions of Dgbv Algebras from Lie Algebras
We give some constructions of diierential Gerstenhaber-Batalin-Vilkovisky algebras from a class of Lie algebras. In our construction, we make use of the solutions to the classical Yang-Baxter equations, and ideas from Poisson geometry. A graded commutative algebra (A; ^) with a bracket ] of degree?1 is called a G-algebra (Gerstenhaber algebra) if: (a) (A1]; ]) is a Lie algebra, where A1] is A w...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2007
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/41/1/015201