arXiv subjects

Xiuli Bian

Publications and source records attributed to Xiuli Bian.

3 recordsLinked to original sources

arXiv2026

The Hochschild cohomlogy ring of a self-injective Nakayama algebra is a Batalin-Vilkovisky algebra

Lambre, Zhou and Zimmermann showed that the Hochschild cohomology ring of a Frobenius algebra with semisimple Nakayama automorphism is a Batalin-Vilkovisky algebra. They asked whether the semisimplicity condition is necessary. In this paper, we show that for a self-injective Nakayama algebra, the Hochschild cohomology ring is always a Batalin-Vilkovisky algebra. In course of proofs, we correct some inaccuracies in the literature, hoping not to introduce new errors.

math.KT↗

arXiv2026

Hochschild cohomology of graded skew-gentle algebras: Gerstenhaber algebra structure and geometric interpretation

In this paper we calculate the Hochschild cohomology of graded skew-gentle algebras, together with its structure as graded commutative algebra under the cup product and its Lie algebra structure given by the Gerstenhaber bracket. One of the results of this paper is that for graded skew-gentle algebras and thus also for partially wrapped Fukaya categories of orbifold surfaces with stops, their Hochschild cohomology is encoded in the underlying graded surface.

math.RT↗

arXiv2026

$A_{\infty}$-structures on the additive decomposition of the Tate-Hochschild cohomology of a finite group algebra

Firstly, for a finite group algebra, we provide a computational framework $\widehat{m}_n$ for the Tate-Hochschild cochain complex in terms of the additive decomposition, by decomposing each planar n-ary tree into local two children and local three children. Secondly, we give all $\widehat{m}_2$ formulas of the Tate-Hochschild cochain complex in terms of the additive decomposition. Thirdly, we give explicit $A_{\infty}$-multiplication formulas for both the Hochschild cochain complex and the Hochschild chain complex under additive decompositions. Finally, we give $A_{\infty}$-multiplication formulas in the context of abelian groups.

math.KT↗