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Failure of flatness over finite-dimensional Hopf subalgebras
Serge Skryabin
It is proved in this paper that for any finite-dimensional nonsemisimple Hopf algebra there exists a Hopf algebra containing as a Hopf subalgebra such that is not f…
Hecke symmetries associated with twisted polynomial algebras in 3 indeterminates
Nikita Shishmarov, Serge Skryabin
We consider Hecke symmetries on a 3-dimensional vector space with the associated R-symmetric algebra isomorphic to the polynomial algebra twisted by an automorphis…
Hecke symmetries associated with the polynomial algebra in 3 commuting indeterminates
Serge Skryabin
It is shown in the paper that each Hecke symmetry R with the R-symmetric algebra freely generated by 3 commuting elements is determined by a bivector and a symmetric bilinear form…
Hecke symmetries: an overview of Frobenius properties
Serge Skryabin
This paper improves several previously known results. First, the results describing the R-skewsymmetric algebra and the quadratic dual of the R-symmetric algebra as Frobenius algeb…
On the graded algebras associated with Hecke symmetries, II. The Hilbert series
Serge Skryabin
This paper continues the work which attempts to understand the general properties of the graded algebras associated with Hecke symmetries without a restriction on the parameter q o…
On the graded algebras associated with Hecke symmetries
Serge Skryabin
We consider quantum symmetric algebras, FRT bialgebras and, more generally, intertwining algebras for pairs of Hecke symmetries which represent quantum hom-spaces. The paper makes…