Displaying similar documents to “Self-equivalences of the derived category of Brauer tree algebras with exceptional vertex.”

Mutating seeds: types 𝔸 and 𝔸 ˜ .

Ibrahim Assem, Christophe Reutenauer (2012)

Annales mathématiques Blaise Pascal

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In the cases 𝔸 and 𝔸 ˜ , we describe the seeds obtained by sequences of mutations from an initial seed. In the 𝔸 ˜ case, we deduce a linear representation of the group of mutations which contains as matrix entries all cluster variables obtained after an arbitrary sequence of mutations (this sequence is an element of the group). Nontransjective variables correspond to certain subgroups of finite index. A noncommutative rational series is constructed, which contains all this information. ...

Euclidean components for a class of self-injective algebras

Sarah Scherotzke (2009)

Colloquium Mathematicae

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We determine the length of composition series of projective modules of G-transitive algebras with an Auslander-Reiten component of Euclidean tree class. We thereby correct and generalize a result of Farnsteiner [Math. Nachr. 202 (1999)]. Furthermore we show that modules with certain length of composition series are periodic. We apply these results to G-transitive blocks of the universal enveloping algebras of restricted p-Lie algebras and prove that G-transitive principal blocks only...

Tree algebras: An algebraic axiomatization of intertwining vertex operators

Igor Kříž, Yang Xiu (2012)

Archivum Mathematicum

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We describe a completely algebraic axiom system for intertwining operators of vertex algebra modules, using algebraic flat connections, thus formulating the concept of a tree algebra. Using the Riemann-Hilbert correspondence, we further prove that a vertex tensor category in the sense of Huang and Lepowsky gives rise to a tree algebra over ℂ . We also show that the chiral WZW model of a simply connected simple compact Lie group gives rise to a tree algebra over ℚ .

Left-sided quasi-invertible bimodules over Nakayama algebras

Zygmunt Pogorzały (2005)

Open Mathematics

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Bimodules over triangular Nakayama algebras that give stable equivalences of Morita type are studied here. As a consequence one obtains that every stable equivalence of Morita type between triangular Nakayama algebras is a Morita equivalence.