MIT Combinatorics Seminar

Positive 2-algebras and the problem on dilation of comultiplication

Anatoly Vershik  (St. Petersburg Department of Steklov Institute of Mathematics)

Tuesday, March 13, 2007    4:15 pm    Room 2-139   (Note unusual day and room!)


We define a class of algebraic systems which is similar to bialgebras and Hopf algebras. We call them positive involutive 2-algebras. One typical example is Hecke algebra. Algebraic combinatorics give many other examples. The problem is to imbed such algebras into a bilagebra (or Hopf algebra) as subobjects or to prove that there are no such dilations. There are at least two rigorous meanings of the notion of "subobject" of bialgebras. The simpliest examples of dilation will be done. The talk is based on the paper math.QA/0702486 in arXiv.