Sep
01
Wednesday, September 7, 2011, 10:10 a.m., in BA 6183
PhD Candidate: Travis Squires
PhD Advisor: Sergey Arkhipov
Thesis Title: Lie 2-Algebras as Homotopy Algebras Over a Quadratic Operad
(http://www.pispace.org/thesis/Thesis-Squires.pdf)
We begin our discussion by introducing some notions from operad
theory; in particular we discuss homotopy algebras over a quadratic
operad. We then proceed to describe Lie 2-algebras as homotopy
algebras over a given quadratic operad using a theorem of Ginzburg
and Kapranov. Next we briefly discuss the structure of a braided
monoidal category. Following this, motivated by our discussion of
braided monoidal categories, a new structure is introduced which
we call a commutative 2-algebra. As with the lie 2-algebra
case we show how a commutative 2-algebra can be seen as a
homotopy algebra over a particular quadratic operad. Finally
some technical results used in previous theorems are mentioned.
In discussing these technical results we apply some ideas about
distributive laws and Koszul operads.
no comment as of now