1,528 research outputs found
Projectivity and freeness over comodule algebras
Let H be a Hopf algebra and A an H-simple right H-comodule algebra. It is
shown that under certain hypotheses every (H,A)-Hopf module is either
projective or free as an A-module and A is either a quasi-Frobenius or a
semisimple ring. As an application it is proved that every weakly finite (in
particular, every finite dimensional) Hopf algebra is free both as a left and a
right module over its finite dimensional right coideal subalgebras, and the
latter are Frobenius algebras. Similar results are obtained for H-simple
H-module algebras.Comment: plain tex, 28p
On the graded algebras associated with Hecke symmetries
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 an attempt to investigate Koszulness and
Gorensteinness of those graded algebras without a restriction on the parameter
q of the Hecke relation used earlier. When q is a root of 1, positive results
require a restriction on the indecomposable modules for the Hecke algebras of
type A that can occur as direct summands of representations in the tensor
powers of the base space.Comment: plain Te
Stability of multi-parameter solitons: Asymptotic approach
General asymptotic approach to the stability problem of multi-parameter
solitons in Hamiltonian systems has been developed. It has been shown that asymptotic study of the
soliton stability can be reduced to the calculation of a certain sequence of
the determinants, where the famous determinant of the matrix consisting from
the derivatives of the system invariants with respect to the soliton parameters
is just the first in the series. The presented approach gives first analytical
criterion for the oscillatory instability and also predicts novel stationary
instability. Higher order approximations allow to calculate corresponding
eigenvalues with arbitrary accuracy.Comment: to appear in Physica
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