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The fundamental theorem and Maschke's theorem in the category of relative Hom-Hopf modules

Yuanyuan Chen, Zhongwei Wang, Liangyun Zhang (2016)

Colloquium Mathematicae

We introduce the concept of relative Hom-Hopf modules and investigate their structure in a monoidal category ̃ ( ℳ k ) . More particularly, the fundamental theorem for relative Hom-Hopf modules is proved under the assumption that the Hom-comodule algebra is cleft. Moreover, Maschke’s theorem for relative Hom-Hopf modules is established when there is a multiplicative total Hom-integral.

The structure of split regular Hom-Poisson algebras

María J. Aragón Periñán, Antonio J. Calderón Martín (2016)

Colloquium Mathematicae

We introduce the class of split regular Hom-Poisson algebras formed by those Hom-Poisson algebras whose underlying Hom-Lie algebras are split and regular. This class is the natural extension of the ones of split Hom-Lie algebras and of split Poisson algebras. We show that the structure theorems for split Poisson algebras can be extended to the more general setting of split regular Hom-Poisson algebras. That is, we prove that an arbitrary split regular Hom-Poisson algebra is of the form = U + ∑ j I j with U...

The variety of dual mock-Lie algebras

Luisa M. Camacho, Ivan Kaygorodov, Viktor Lopatkin, Mohamed A. Salim (2020)

Communications in Mathematics

We classify all complex 7 - and 8 -dimensional dual mock-Lie algebras by the algebraic and geometric way. Also, we find all non-trivial complex 9 -dimensional dual mock-Lie algebras.

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