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Le : 24/03/2010 15h15
Par : Sergei DUZHIN (IHES)
Lieu :
Lien web :
Résumé : A necklace is an arrangement of colored beads along a circle considered up to rotations. We will speak about various applications of necklaces in mathematics: 1. Primitive n-colored necklaces are in 1-1 correspondence with Lyndon words (which form a bases of the free Lie algebra on n generators). 2. Primitive necklaces are in 1-1 correspondence with irreducible polynomials over a finite field. 3. Free commutative algebra generated by necklaces can be interpreted as the ad-invariant subspace in the tensor power of the symmetric algebra over the Lie algebra gl_n, so that there is a weight system (in the sense of Vasiliev invariants) with values in the necklace algebra. (That's where my personal interest in the subject stems from.) 4. Necklaces are also used in the study of the algebra of multiple zeta