Geometric approach to Hall algebra of representations of Quivers over local ring

Abstract

By using perverse sheaves on representation spaces of quivers over $k[t]/(t^n)$ and jet schemes over flag varieties, we construct a geometric composition algebra $\mathbf{K}$ under Lusztig's framework on geometric realizations of the negative part of quantum algebras. Simple perverse sheaves in $\mathbf{K}$ form the canonical basis of $\mathbf{K}$. The relationships among the algebra $\mathbf{K}$, the composition algebra of locally projective representations of quivers over $k[t]/(t^n)$ and quantum generalized Kac-Moody algebra are provided.

Simplify some proofs and some other revisions on the earlier version

References in corpus (4)

• Jet Schemes of Locally Complete Intersection Canonical Singularities
• Notes on Perverse Sheaves and Vanishing Cycles
• Notes on affine canonical and monomial bases
• A geometric version of BGP reflection functors

Cited by in corpus (1)

• The finite EI categories of Cartan type