616 research outputs found
Small Bialgebras with a Projection: Applications
In this paper we continue the investigation started in [A.M.St.-Small],
dealing with bialgebras with an -bilinear coalgebra projection over an
arbitrary subbialgebra with antipode. These bialgebras can be described as
deformed bosonizations R#_{\xi} H of a pre-bialgebra by with a
cocycle . Here we describe the behavior of in the case when is
f.d. and thin i.e. it is connected with one dimensional space of primitive
elements. This is used to analyze the arithmetic properties of . Meaningful
results are obtained when is cosemisimple. By means of Ore extension
construction, we provide some examples of atypical situations (e.g. the
multiplication of is not -colinear or is non-trivial)
Integrals, quantum Galois extensions and the affineness criterion for quantum Yetter-Drinfel'd modules
We introduce and study a general concept of integral of a threetuple (H, A,
C), where H is a Hopf algebra acting on a coalgebra C and coacting on an
algebra A. In particular, quantum integrals associated to Yetter-Drinfel'd
modules are defined. Let A be an H-bicomodule algebra, be the
category of (generalized) Yetter-Drinfel'd modules and the subalgebra of
coinvariants of the Verma structure of . We introduce the concept of quantum
Galois extensions and we prove the affineness criterion in a quantum version.Comment: latex 32 pg. J. Algebra, to appea
Categories of comodules and chain complexes of modules
Let \lL(A) denote the coendomorphism left -bialgebroid associated to a
left finitely generated and projective extension of rings with
identities. We show that the category of left comodules over an epimorphic
image of \lL(A) is equivalent to the category of chain complexes of left
-modules. This equivalence is monoidal whenever is commutative and
is an -algebra. This is a generalization, using entirely new tools, of
results by B. Pareigis and D. Tambara for chain complexes of vector spaces over
fields. Our approach relies heavily on the non commutative theory of Tannaka
reconstruction, and the generalized faithfully flat descent for small additive
categories, or rings with enough orthogonal idempotents.Comment: The title has been changed, the first part is removed and the
construction of the coendomorphim bialgebroid is now freely used in the
statement of the main Theorem
When is R-gr equivalent to the category of modules?
AbstractIn the first part of this paper, we characterize graded rings R=⊕σ∈GRσ for which the category R-gr is equivalent with a category of modules over a certain ring.In the second part, sufficient conditions are given for the following implication to hold: if R-gr is equivalent with R1-mod (1 is the unit element of G), then R is a strongly graded ring
Braided Bialgebras of Type One
Braided bialgebras of type one in abelian braided monoidal categories are
characterized as braided graded bialgebras which are strongly
-graded both as an algebra and as a coalgebra
Braided Bialgebras of Hecke-type
The paper is devoted to prove a version of Milnor-Moore Theorem
for connected braided bialgebras that are infinitesimally
cocommutative. Namely in characteristic different from , we
prove that, for a given connected braided bialgebra
which is infinitesimally -cocommutative for some element that is not a root of one in the base field, then the infinitesimal braiding of
is of Hecke-type of mark and is isomorphic as a braided bialgebra to the symmetric algebra of the braided subspace of its primitive elements
Small bialgebras with a projection
AbstractLet A be a bialgebra with an H-bilinear coalgebra projection over an arbitrary subbialgebra H with antipode. In characteristic zero, we completely describe the bialgebra structure of A whenever H is either f.d. or cosemisimple and the H-coinvariant part R of A is connected with one-dimensional space of primitive elements
Modulation by internal protons of native cyclic nucleotide-gated channels from retinal rods
Ion channels directly activated by cyclic nucleotides are present in the plasma membrane of retinal rod outer segments. These channels can be modulated by several factors including internal pH (pH(i)). Native cyclic nucleotide-gated channels were studied in excised membrane patches from the outer segment of retinal rods of the salamander. Channels were activated by cGMP or cAMP and currents as a function of voltage and cyclic nucleotide concentrations were measured as pH(i) was varied between 7.6 and 5.0. Increasing internal proton concentrations reduced the current activated by cGMP without modifying the concentration (K(1/2)) of cGMP necessary for half-activation of the maximal current. This effect could be well described as a reduction of single-channel current by protonation of a single acidic residue with a pK(1) of 5.1. When channels were activated by cAMP a more complex phenomenon was observed. K(1/2) for cAMP decreased by increasing internal proton concentration whereas maximal currents activated by cAMP increased by lowering pH(i) from 7.6 to 5.7-5.5 and then decreased from pH(i) 5.5 to 5.0. This behavior was attributed both to a reduction in single-channel current as measured with cGMP and to an increase in channel open probability induced by the binding of three protons to sites with a pK(2) of 6
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