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SUMMARY:Lie\, associative and commutative quasi-isomorphism - Dan Petersen
 \, Stockholm
DTSTART:20190227T160000Z
DTEND:20190227T170000Z
UID:TALK116725@talks.cam.ac.uk
CONTACT:Oscar Randal-Williams
DESCRIPTION:We present two "Koszul dual" theorems: (A) If two commutative 
 dg algebras in characteristic zero are quasi-isomorphic as dg algebras\, t
 hen they are also quasi-isomorphic as commutative dg algebras. (B) If two 
 dg Lie algebras in characteristic zero have universal enveloping algebras 
 which are quasi-isomorphic as dg algebras\, then the dg Lie algebras are t
 hemselves quasi-isomorphic. Theorem B says in particular that two Lie alge
 bras in characteristic zero (with no grading or differential) are isomorph
 ic if and only if their universal enveloping algebras are isomorphic as al
 gebras\; even this result is new and answers an open question. Via the wor
 k of Quillen and Sullivan\, these theorems have immediate consequences in 
 rational homotopy theory: two simply connected spaces have the same ration
 al homotopy type if and only if their algebras of rational cochains are qu
 asi-isomorphic\, if and only if the algebras of rational chains on their M
 oore loop spaces are quasi-isomorphic. (Joint work with R. Campos\, D. Rob
 ert-Nicoud\, F. Wierstra)
LOCATION:MR13
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