arXiv subjects

Shiquan Ruan

Publications and source records attributed to Shiquan Ruan.

41 records · Page 3Linked to original sources

arXiv2017

Exceptional sequences and Drinfeld double Hall algebras

Let $\A$ be a finitary hereditary abelian category and $D(\A)$ be its reduced Drinfeld double Hall algebra. By giving explicit formulas in $D(\A)$ for left and right mutations, we show that the subalgebras of $D(\A)$ generated by exceptional sequences are invariant under mutation equivalences. As an application, we obtain that if $\A$ is the category of finite dimensional modules over a finite dimensional hereditary algebra, or the category of coherent sheaves on a weighted projective line, the double composition algebra of $\A$ is generated by any complete exceptional sequence. Moreover, for the Lie algebra case, we also have paralleled results.

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arXiv2016

On derived Hall numbers for tame quivers

In the present paper we study the derived Hall algebra for the bounded derived category of the nilpotent representations of a tame quiver over a finite field. We show that for any three given objects in the bounded derived category, the associated derived Hall numbers are given by a rational function in the cardinalities of ground fields.

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arXiv2015

Hall polynomials for tame type

In the present paper we prove that Hall polynomial exists for each triple of decomposition sequences which parameterize isomorphism classes of coherent sheaves of a domestic weighted projective line $\mathbb X$ over finite fields. These polynomials are then used to define the generic Ringel--Hall algebra of $\mathbb X$ as well as its Drinfeld double. Combining this construction with a result of Cramer, we show that Hall polynomials exist for tame quivers, which not only refines a result of Hubery, but also confirms a conjecture of Berenstein and Greenstein.

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arXiv2013

Tilting bundles and the "missing part" on the weighted projective line of type $(2, 2, n)$

This paper classifies all the tilting bundles in the category of coherent sheaves on the weighted projective line of weight type $(2, 2, n)$, and investigates the abelianness of the "missing part" from the category of coherent sheaves to the category of finitely generated right modules on the associated tilted algebra for each tilting bundle.

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arXiv2013

Tilting objects in the stable category of vector bundles on the weighted projective line of type (2,2,2,2;λ)

We construct a tilting object for the stable category of vector bundles on a weighted projective line X of type (2,2,2,2;λ), consisting of five rank two bundles and one rank three bundle, whose endomorphism algebra is a canonical algebra associated with X of type (2,2,2,2).

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