3,893 research outputs found
The dual and the double of a Hopf algebroid are Hopf algebroids
Let be a -bialgebra in the sense of Takeuchi. We show that if
is -Hopf, and if fulfills the finiteness condition necessary to
define its skew dual , then the coopposite of the latter is
-Hopf as well.
If in addition the coopposite -bialgebra of is -Hopf,
then the coopposite of the Drinfeld double of is -Hopf, as is the
Drinfeld double itself, under an additional finiteness condition
Frobenius-Schur indicators for some fusion categories associated to symmetric and alternating groups
We calculate Frobenius-Schur indicator values for some fusion categories
obtained from inclusions of finite groups , where more concretely
is symmetric or alternating, and is a symmetric, alternating or cyclic
group. Our work is strongly related to earlier results by
Kashina-Mason-Montgomery, Jedwab-Montgomery, and Timmer for bismash product
Hopf algebras obtained from exact factorizations of groups. We can generalize
some of their results, settle some open questions and offer shorter proofs;
this already pertains to the Hopf algebra case, while our results also cover
fusion categories not associated to Hopf algebras.Comment: 15 page
Serre Theorem for involutory Hopf algebras
We call a monoidal category a Serre category if for any ,
such that C\ot D is semisimple, and are
semisimple objects in . Let be an involutory Hopf algebra,
, two -(co)modules such that is (co)semisimple as a
-(co)module. If (resp. ) is a finitely generated projective
-module with invertible Hattory-Stallings rank in then (resp. )
is (co)semisimple as a -(co)module. In particular, the full subcategory of
all finite dimensional modules, comodules or Yetter-Drinfel'd modules over
the dimension of which is invertible in are Serre categories.Comment: a new version: 8 page
Modified Affine Hecke Algebras and Drinfeldians of Type A
We introduce a modified affine Hecke algebra \h{H}^{+}_{q\eta}({l})
(\h{H}_{q\eta}({l})) which depends on two deformation parameters and
. When the parameter is equal to zero the algebra
\h{H}_{q\eta=0}(l) coincides with the usual affine Hecke algebra
\h{H}_{q}(l) of type , if the parameter q goes to 1 the algebra
\h{H}^{+}_{q=1\eta}(l) is isomorphic to the degenerate affine Hecke algebra
\Lm_{\eta}(l) introduced by Drinfeld. We construct a functor from a category
of representations of into a category of representations of
Drinfeldian which has been introduced by the first author.Comment: 11 pages, LATEX. Contribution to Proceedings "Quantum Theory and
Symmetries" (Goslar, July 18-22, 1999) (World Scientific, 2000
Homfly Polynomials of Generalized Hopf Links
Following the recent work by T.-H. Chan in [HOMFLY polynomial of some
generalized Hopf links, J. Knot Theory Ramif. 9 (2000) 865--883] on reverse
string parallels of the Hopf link we give an alternative approach to finding
the Homfly polynomials of these links, based on the Homfly skein of the
annulus. We establish that two natural skein maps have distinct eigenvalues,
answering a question raised by Chan, and use this result to calculate the
Homfly polynomial of some more general reverse string satellites of the Hopf
link.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-2.abs.htm
Yetter-Drinfeld-Long bimodules are modules
Let be a finite dimensional bialgebra. In this paper, we prove that the
category of Yetter-Drinfeld-Long bimodules is isomorphic to the Yetter-Drinfeld
category over the tensor product bialgebra H\o H^* as monoidal category.
Moreover if is a Hopf algebra with bijective antipode, the isomorphism is
braided.Comment: to appear in Czechoslovak Mathematical Journa
Towards a sufficient criterion for collapse in 3D Euler equations
A sufficient integral criterion for a blow-up solution of the Hopf equations
(the Euler equations with zero pressure) is found. This criterion shows that a
certain positive integral quantity blows up in a finite time under specific
initial conditions. Blow-up of this quantity means that solution of the Hopf
equation in 3D can not be continued in the Sobolev space for
infinite time
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