16-18 October 2013
Université d'Angers
Europe/Paris timezone

Derived representation schemes, Lie (co)homology and a Macdonald type conjecture

18 Oct 2013, 11:45
Amphi L005 (bâtiment L) (Université d'Angers)

Amphi L005 (bâtiment L)

Université d'Angers

Université d'Angers, 2 Boulevard Lavoisier, 49045 Angers cedex 01
Exposé de recherche sur invitation Topologie algébrique et applications


Dr Ajay Ramadoss (IU Bloomington)


We explicitly relate the homotopy commutative DGA corresponding to the derived representation scheme DRep_n(A) of an augmented algebra A to the Chevalley-Eilenberg homology of Lie coalgebras arising out of certain DG coalgebras associated with A. As a result, we can construct a natural map (of homotopy commutative DGAs) from DRep_n(A) to the n-th symmetric power of DRep_1(A). The latter map can be viewed as a derived Harish-Chandra homomorphism. For A a polynomial algebra, we obtain explicit formulas for the composition of the derived Harish-Chandra homomorphism with the higher traces from (reduced) cyclic homology. We further conjecture that when A=k[x,y], this map is in fact, a quasi-isomorphism. Time permitting, we will try to explain how our conjecture, if true leads to a new Macdonald type identity. (This is joint work with Yuri Berest, Giovanni Felder and Aliaksandr Patotski.)
Mots Clés / Keywords Derived representation scheme; Lie cohomology

Primary author

Dr Ajay Ramadoss (IU Bloomington)

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