Vladimir Dotsenko (Université du Luxembourg, Luxembourg), Rewriting methods for associative algebras and operads


  • Feb. 28, 2012, 9:00 - 10:30
  • Feb. 29, 2012, 11:00 - 12:30
  • March 2, 2012, 9:00 - 10:30


I. Associative algebras and Groebner bases. Bergman's Diamond lemma, and an algorithm for constructing Groebner bases that it implies. (Digression: the case of commutative algebras, and systems of polynomial equations.)

II. Symmetric and nonsymmetric operads. Examples. Generalisation of Groebner bases for the case of nonsymmetric operad. Trees and word sequences. Failure of rewriting methods for symmetric operads.

III. Shuffle operads. Monoidality of the forgetful functor, and its consequences for the symmetric case. Admissible ordering of shuffle trees. Examples of Groebner bases. Koszul duality and Hoffbeck's PBW criterion.

IV. Groebner bases and free resolutions. Module resolutions: the theorem of Anick--Groves--Squier. Algebra resolutions. A-infinity algebras.