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Quasitriangular Hom-Hopf algebras

Yuanyuan Chen, Zhongwei Wang, Liangyun Zhang (2014)

Colloquium Mathematicae

A twisted generalization of quasitriangular Hopf algebras called quasitriangular Hom-Hopf algebras is introduced. We characterize these algebras in terms of certain morphisms. We also give their equivalent description via a braided monoidal category ̃ ( H ℳ ) . Finally, we study the twisting structure of quasitriangular Hom-Hopf algebras by conjugation with Hom-2-cocycles.

Quasitriangular Hopf group algebras and braided monoidal categories

Shiyin Zhao, Jing Wang, Hui-Xiang Chen (2014)

Czechoslovak Mathematical Journal

Let π be a group, and H be a semi-Hopf π -algebra. We first show that the category H ℳ of left π -modules over H is a monoidal category with a suitably defined tensor product and each element α in π induces a strict monoidal functor F α from H ℳ to itself. Then we introduce the concept of quasitriangular semi-Hopf π -algebra, and show that a semi-Hopf π -algebra H is quasitriangular if and only if the category H ℳ is a braided monoidal category and F α is a strict braided monoidal functor for any α ∈ π . Finally,...

Quasitrivial semimodules. IV.

Tomáš Kepka, Petr Němec (2013)

Acta Universitatis Carolinae. Mathematica et Physica

Almost quasitrivial and critical semimodules are studied.

Quasitrivial semimodules. V.

Tomáš Kepka, Petr Němec (2013)

Acta Universitatis Carolinae. Mathematica et Physica

Critical semimodules over congruence-simple semirings are studied.

Quasitrivial semimodules. VI.

Tomáš Kepka, Petr Němec (2013)

Acta Universitatis Carolinae. Mathematica et Physica

The paper continues the investigation of quasitrivial semimodules and related problems. In particular, endomorphisms of semilattices are investigated.

Quasitrivial semimodules. VII.

Tomáš Kepka, Petr Němec (2013)

Acta Universitatis Carolinae. Mathematica et Physica

The paper continues the investigation of quasitrivial semimodules and related problems. In particular, strong endomorphisms of semilattices are studied.

Quiver bialgebras and monoidal categories

Hua-Lin Huang, Blas Torrecillas (2013)

Colloquium Mathematicae

We study bialgebra structures on quiver coalgebras and monoidal structures on the categories of locally nilpotent and locally finite quiver representations. It is shown that the path coalgebra of an arbitrary quiver admits natural bialgebra structures. This endows the category of locally nilpotent and locally finite representations of an arbitrary quiver with natural monoidal structures from bialgebras. We also obtain theorems of Gabriel type for pointed bialgebras and hereditary finite pointed...

Quiver varieties and the character ring of general linear groups over finite fields

Emmanuel Letellier (2013)

Journal of the European Mathematical Society

Given a tuple ( 𝒳 1 , ... , 𝒳 k ) of irreducible characters of G L n ( F q ) we define a star-shaped quiver Γ together with a dimension vector v . Assume that ( 𝒳 1 , ... , 𝒳 k ) is generic. Our first result is a formula which expresses the multiplicity of the trivial character in the tensor product 𝒳 1 ⊗ ⋯ ⊗ 𝒳 k as the trace of the action of some Weyl group on the intersection cohomology of some (non-affine) quiver varieties associated to ( Γ , v ) . The existence of such a quiver variety is subject to some condition. Assuming that this condition is satisfied, we...

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