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A remark on quiver varieties and Weyl groups

Andrea Maffei (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In this paper we define an action of the Weyl group on the quiver varieties M m , λ ( v ) with generic ( m , λ ) .

Mutating seeds: types 𝔸 and 𝔸 ˜ .

Ibrahim Assem, Christophe Reutenauer (2012)

Annales mathématiques Blaise Pascal

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.

On fuzzification of the notion of quantaloid

Sergey A. Solovyov (2010)


The paper considers a fuzzification of the notion of quantaloid of K. I. Rosenthal, which replaces enrichment in the category of -semilattices with that in the category of modules over a given unital commutative quantale. The resulting structures are called quantale algebroids. We show that their constitute a monadic category and prove a representation theorem for them using the notion of nucleus adjusted for our needs. We also characterize the lattice of nuclei on a free quantale algebroid. At...

Rigidity of generalized Verma modules

Oleksandr Khomenko, Volodymyr Mazorchuk (2002)

Colloquium Mathematicae

We prove that generalized Verma modules induced from generic Gelfand-Zetlin modules, and generalized Verma modules associated with Enright-complete modules, are rigid. Their Loewy lengths and quotients of the unique Loewy filtrations are calculated for the regular block of the corresponding category 𝒪(𝔭,Λ).

The structures of Hopf * -algebra on Radford algebras

Hassan Suleman Esmael Mohammed, Hui-Xiang Chen (2019)

Czechoslovak Mathematical Journal

We investigate the structures of Hopf * -algebra on the Radford algebras over . All the * -structures on H are explicitly given. Moreover, these Hopf * -algebra structures are classified up to equivalence.

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