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arXiv · 1012.5257

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

Zhaobing Fan
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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.

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BibTeXRIS

Zhaobing Fan. 2014-10-22. Geometric approach to Hall algebra of representations of Quivers over local ring. https://arxiv.org/abs/1012.5257

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