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Bohan Xing

Publications and source records attributed to Bohan Xing.

11 recordsLinked to original sources
arXiv2026

Classification of Brauer graph algebras under stable equivalence of Morita type

The classification of Brauer graph algebras under derived equivalence was recently given by Opper and Zvonareva. In this paper, we prove that two Brauer graph algebras are derived equivalent if and only if they are stably equivalent of Morita type. As an application, we show that every stable Picard group orbit of simple-images of Morita type contains a liftable representative. Moreover, we give a new proof of the fact that Brauer graph algebras are closed up to semisimple summands under stable equivalence of Morita type.

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arXiv2026

Brauer graph algebras are closed under stable equivalence of Morita type

We study stable equivalences of Brauer graph algebras. In particular, we prove that Brauer graph algebras are closed up to semisimple summands under stable equivalence of Morita type. As a consequence, we reprove the result of Antipov and Zvonareva that Brauer graph algebras are closed under derived equivalence. As a byproduct, we get a solution of the reconstruction problem posed by Rickard and Rouquier for algebras stably equivalent of Morita type to Brauer graph algebras.

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arXiv2026

A classification of derived-discrete graded algebras

A finite-dimensional algebra is derived-discrete, in the sense of Vossieck, precisely when it is a piecewise hereditary algebra of Dynkin type or a gentle one-cycle algebra not satisfying the clock condition. Building on the discrete triangulated categories of Broomhead, Pauksztello, and Ploog, we study derived-discreteness for locally finite non-positively graded algebras, regarded as connective locally finite dg algebras with trivial differential. Our main result extends Vossieck's classification to this setting: such a graded algebra is derived-discrete if and only if it is graded Morita equivalent to a piecewise hereditary algebra of Dynkin type, or it is a graded gentle one-cycle algebra not satisfying the graded clock condition. Along the way, using surface models we prove the conjecture of Kalck and Yang that the graded clock condition is invariant under derived equivalence. We also establish a restriction on semi-orthogonal decompositions of the bounded derived category of a path algebra of Dynkin type $D$.

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arXiv2026

Two-term tilting complexes of biserial fractional Brauer graph algebras

Brauer graph algebras form a classical class of symmetric algebras with well-structured combinatorial properties and geometric models. Recently, they have been generalized to biserial fractional Brauer graph algebras, which can be regarded as a self-injective version of the classical Brauer graph algebras. In this paper, we show that the skew group algebras of biserial fractional Brauer graph algebras induced by the Nakayama automorphism are in fact skew-Brauer graph algebras. We then study two-term tilting complexes and Kauer moves for biserial fractional Brauer graph algebras. Moreover, we prove that a biserial fractional Brauer graph algebra is tilting-discrete if and only if its reduced form (which is a Brauer graph algebra) is tilting-discrete. Finally, we show that tilting-discrete biserial fractional Brauer graph algebras are closed under derived equivalence.

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arXiv2026

Invariants of derived equivalences for admissible fractional Brauer graph algebras

Characterizing derived equivalences between algebras via combinatorial structures has recently become a popular topic. In this paper, we study admissible fractional Brauer graph algebras, a new subclass of self-injective special biserial algebras, and provide several easily checkable combinatorial invariants for derived equivalences between them. In particular, we show that these algebras can be viewed as repetitive algebras and $r$-fold trivial extensions of gentle algebras.

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arXiv2026

The second Hochschild cohomology and deformations of Brauer graph algebras

In this paper, we give an explicit description about the second Hochschild cohomology groups of bipartite Brauer graph algebras with trivial grading. Based on this, we provide geometric interpretations of deformations associated to some standard cocycles in terms of the surface models of Brauer graph algebras.

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arXiv2024

Quasi-biserial algebras, special quasi-biserial algebras and symmetric fractional Brauer graph algebras

Biserial algebras are a classical class in the representation theory of algebras, generalizing Nakayama algebras. They were further generalized by Green and Schroll to multiserial algebras, which share many structural properties with biserial algebras. Inspired by their motivation, we introduce another generalization, called quasi-biserial algebras. We show that this class retains fundamental properties of classical biserial algebras. In the symmetric special case, we establish a correspondence with labeled ribbon graphs equipped with multiplicities, providing a combinatorial model for the algebras. Furthermore, we prove that Kauer moves on these graphs, interpreted as mutations of labeled ribbon graphs, induce derived equivalences between the associated symmetric special quasi-biserial algebras.

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arXiv2024

Trivial extensions of monomial algebras are symmetric fractional Brauer configuration algebras

By providing equivalent definitions of fractional Brauer configuration algebras in certain special cases, we associate to each monomial algebra some combinatorial data called a fractional Brauer configuration, from which we construct a corresponding fractional Brauer configuration algebra. We show that this algebra is isomorphic to the trivial extension of the given monomial algebra. Furthermore, we establish a one-to-one correspondence between the isomorphism classes of monomial algebras and the equivalence classes of pairs consisting of a symmetric fractional Brauer configuration algebra of type S with a free fractional-degree function and an admissible cut on it.

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arXiv2024

A note on higher structures on the complexes associated to quiver algebras with applications to toupie algebras

In this paper, we summarize a general method of transforming DG structures into higher structures on the various complexes related to the reduced bar resolution of a given quiver algebra using algebraic Morse theory. As an application, we describe the $A_\infty$-structures of toupie algebras. Additionally, for certain special toupie algebras, we also prove that their double homological duals are isomorphic to their associated graded algebras.

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