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arXiv · 2511.22051

Geometric realizations of Ringel-Hall algebras of continuous quivers of type $A$

Minghui Zhao
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Abstract

Lusztig introduced the geometric realizations of quantum groups associated to finite quivers and defined their canonical bases. Sala and Schiffmann introduced the Ringel-Hall algebra of line and realized it as the direct limit of Ringel-Hall algebras of finite quivers of type $A$. In this paper, we shall give geometric realizations of Ringel-Hall algebras of continuous quivers of type $A$ via the geometric realizations of Lusztig by using the method of approximation given by Sala and Schiffmann.

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Minghui Zhao. 2025-11-27. Geometric realizations of Ringel-Hall algebras of continuous quivers of type $A$. https://arxiv.org/abs/2511.22051

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