DG structures on categorified quantum groups

Acknowledgments
Introduction
	Categorification
	Quantum Groups
	Odd Differentials
		Motivations from link homology theory
		The oddification program
		Covering Kac-Moody algebras
		Differential graded structures on categorified quantum group
		Categorification
	A DG-extension of Symmetric Functions
A DG-Structure on Odd 2-category
	Super dg theory
		Super 2-categories
		Super dg-algebras
		Super dg-categories
		Super dg-2-categories
	Hopfological algebra
		Basic setup
		DG-algebras from the Hopfological perspective
		Decategorification from the Hopfological perspective
		Gaussian integers
	Results on Grothendieck groups of super dg-algebras
		Grothendieck group of a super dg-algebra
		Positively graded dg-algebras
		Grothendieck ring of super dg-2-categories
		Fantastic filtrations
	The odd 2-category for sl(2)
		The odd nilHecke ring
		The odd categorified quantum group
		Additional Relations
	Derivations on the odd 2-category
		Derivations on odd 2-category arising from the fantastic filtration
	Differentials on the odd 2-category
	Quantum sl(2) at a fourth root of unity
		Idempotented quantum sl2
		Small quantum sl2
	Categorification results
		Divided power modules
		The DG-Grothendieck ring
A DG-extension of Symmetric Functions
	The nilHecke algebra
		The definition
	The extended nilHecke algebra
		The definition
		Action on polynomials
		Differentials
	The ring of extended symmetric polynomials
		Definition
		The size of extended symmetric functions
		Structure of the extended nilHecke algebra
		Bases of extn
		Combinatorial identities
	Solomon\'s Theorem
		Superpolynomials and superinvariants
		Action of the extended nilHecke algebra
		Preliminary computations
		NHextn–equivariant isomorphisms
		Example
	Differentials
		The standard differential
		Koszul complex
		Deformed differentials
		Categorification
Conclusions and Future Work
Bibliography