Quotients of Kontsevich's "Lie" Lie algebra
Hot Topics: Galois Theory of Periods and Applications March 27, 2017 - March 31, 2017
Location: MSRI: Simons Auditorium
Galois theory
Galois orbits
Periods
free Lie algebras
Lie algebras
univalent trees
operads
mapping class groups
automorphism groups
filtrations
11Rxx - Algebraic number theory: global fields {For complex multiplication, see 11G15}
14C30 - Transcendental methods, Hodge theory [See also 14D07, 32G20, 32J25, 32S35], Hodge conjecture
17B65 - Infinite-dimensional Lie (super)algebras [See also 22E65]
Conant
We study two quotients of the Lie Lie algebra (the Lie algebra of symplectic derivations of the free Lie algebra), namely the abelianization and the the quotient by the Lie algebra generated by degree 1 elements. The abelianization has a very close connection to the homology of groups of automorphism groups of free groups, whereas the second is the so-called "Johnson cokernel," the cokernel of the Johnson homomorphism defined for mapping class groups of punctured surfaces
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Conant
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