EVENT DETAILS AND ABSTRACT

Title: A Lie algebra for the String group
Speaker: André Henriques
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Abstract:

In "Higher-Dimensional Algebra V: 2-Groups" J. Baez and A. Lauda investigate a correspondence between Lie 2-algebras and Lie 2-groups extending the classical correspondence between Lie algebras and Lie groups. However, their construction is imperfect. According to them, some interesting Lie 2-algebra have no corresponding Lie 2-group.

I'll explain how to modify the definition of Lie 2-group in order to make their correspondence go through. Then, I'll concentrate on the L_2-algebra string(n) := spin(n)\oplus\R[1], with brackets [(X,a), (Y,b)] := ([X,Y], 0) and [(X,a), (Y,b), (Z,c)] := (0, <[X,Y],Z>). The corresponding 2-group is homotopy equivalent to the 3-connected cover String(n) of Spin(n).