Recursos de colección
Project Euclid (Hosted at Cornell University Library) (192.674 recursos)
Bulletin of the Belgian Mathematical Society-Simon Stevin
Bulletin of the Belgian Mathematical Society-Simon Stevin
Jung, Seoung Dal; Liu, Huili
A well-known result by M. Min-Oo et al. states that
there are no nontrivial basic harmonic $r (0<
r
Sadarangani, Kishin; Samet, Bessem
We study the existence of solutions for a new class of integral equations involving a fractional integral with respect to another function. Our techniques are based on the measure of non-compactness concept combined with a generalized version of Darbo's theorem. Some examples are presented to illustrate the obtained results.
Gan, Wee Liang
We give a simple proof that (a generalization of) the complex of injective words has vanishing homology in all except the top degree.
Chatzidakis, Zoé; Perera, Milan
Let $p$ be a prime. In this paper we give a proof of the following
result: A valued field $(K,v)$ of characteristic $p > 0$ is
$p$-henselian if and only if every element of strictly positive
valuation is of the form $x^p - x$ for some $x \in K$.
Böhm, Gabriella; Lack, Stephen
Although multiplier bimonoids in general are not known to correspond to
comonoids in any monoidal category, we classify them in terms of maps from the
Catalan simplicial set to another suitable simplicial set; thus they can be
regarded as (co)monoids in something more general than a monoidal
category (namely, the simplicial set itself).
We analyze the particular simplicial maps corresponding to that class of
multiplier bimonoids which can be regarded as comonoids.
Lentner, Simon; Priel, Jan
In this article we construct three explicit natural subgroups of the
Brauer-Picard group of the category of representations of a
finite-dimensional Hopf algebra. In examples the Brauer Picard group decomposes
into an ordered product of these subgroups, somewhat similar to a Bruhat
decomposition.
Our construction returns for any Hopf algebra three types of braided
autoequivalences and correspondingly three families of invertible bimodule
categories. This gives examples of so-called (2-)Morita
equivalences and defects in topological field theories. We have a closer
look at the case of quantum groups and Nichols algebras and give
interesting applications. Finally, we briefly discuss the three families of
group-theoretic extensions.
Batista, Eliezer
We present a survey of recent developments in the theory of partial actions of groups and Hopf algebras.
Andruskiewitsch, Nicolás; Angiono, Iván; Rossi Bertone, Fiorela
Let ${\mathcal{B}}_{\mathfrak{q}}$ be a finite-dimensional Nichols algebra of diagonal type corresponding to a matrix $\mathfrak{q} \in {\mathbf{k}}^{\theta \times \theta}$.
Let ${\mathcal{L}}_{\mathfrak{q}}$ be the Lusztig algebra associated to ${\mathcal{B}}_{\mathfrak{q}}$.
We present ${\mathcal{L}}_{\mathfrak{q}}$ as an extension (as braided Hopf algebras) of ${\mathcal{B}}_{\mathfrak{q}}$ by ${\mathfrak Z}_{\mathfrak{q}}$ where ${\mathfrak Z}_{\mathfrak{q}}$ is isomorphic to the universal enveloping algebra of a Lie algebra ${\mathfrak{n}}_\mathfrak{q}$. We compute the Lie algebra ${\mathfrak{n}}_{\mathfrak{q}}$ when $\theta = 2$.
Cohen, Miriam; Westreich, Sara
Liu, Gongxiang; Van Oystaeyen, Fred; Zhang, Yinhuo
The quasi-Frobenius-Lusztig kernel ${\operatorname{Q}}\mathbf{u}_{q}(\mathfrak{sl}_{2})$
associated with $\mathfrak{sl}_{2}$ has been constructed in [9]. In this paper we study the representations of this small quasi-quantum group. We give a complete list of non-isomorphic indecomposables and the tensor product decomposition rules for simples and projectives. A description of the Grothendieck ring is also provided.
Schauenburg, Peter
Lie-Rinehart algebras, also known as Lie algebroids, give rise to Hopf algebroids by a universal enveloping algebra construction, much as the universal enveloping algebra of an ordinary Lie algebra gives a Hopf algebra, of infinite dimension. In finite characteristic, the universal enveloping algebra of a restricted Lie algebra admits a quotient Hopf algebra which is finite-dimensional if the Lie algebra is. Rumynin has shown that suitably defined restricted Lie algebroids allow to define restricted universal enveloping algebras that are finitely generated projective if the Lie algebroid is. This note presents an alternative proof and possibly fills a gap that might,...
Janelidze, G.
The connection between categorical and differential Galois theories established by the author (published in 1989) is extended to the context that includes difference Galois theory.
Kadison, Lars
Study of the quotient module of a finite-dimensional Hopf subalgebra pair in order to compute its depth yields a relative Maschke Theorem, in which semisimple extension is characterized as being separable, and is therefore an ordinary Frobenius extension. We study the core Hopf ideal of a Hopf subalgebra, noting that the length of the annihilator chain of tensor powers of the quotient module is linearly related to the depth, if the Hopf algebra is semisimple. A tensor categorical definition of depth is introduced, and a summary from this new point of view of previous results are included. It is shown...
Brzeziński, Tomasz
Rota-Baxter systems are modified by the inclusion of a curvature term. It is shown that, subject to specific properties of the curvature form, curved Rota-Baxter systems $(A,R,S,\omega)$ induce associative and (left) pre-Lie products on the algebra $A$. It is also shown that if both Rota-Baxter operators coincide with each other and the curvature is $A$-bilinear, then the (modified by $R$) Hochschild cohomology ring over $A$ is a curved differential graded algebra.
Chen, Hui-Xiang; Mohammed, Hassen Suleman Esmael; Lin, Weijun; Sun, Hua
In this paper, we compute the projective class rings of the tensor product
$\mathcal{H}_n(q)=A_n(q)\ot A_n(q^{-1})$ of Taft algebras $A_n(q)$ and $A_n(q^{-1})$, and its
cocycle deformations $H_n(0,q)$ and $H_n(1,q)$, where $n>2$ is a positive integer
and $q$ is a primitive $n$-th root of unity. It is shown that the projective class rings $r_p(\mathcal{H}_n(q))$,
$r_p(H_n(0,q))$ and $r_p(H_n(1,q))$ are commutative rings generated by three elements, three elements and
two elements subject to some relations, respectively.
It turns out that even $\mathcal{H}_n(q)$, $H_n(0,q)$ and $H_n(1,q)$
are cocycle twist-equivalent to each other, they are of different representation types: wild, wild and tame, respectively.
Montoli, Andrea; Rodelo, Diana; Van der Linden, Tim
We give a new sufficient condition for the normal extensions in an
admissible Galois structure to be reflective. We then show that
this condition is indeed fulfilled when $\mathbb{X}$ is the (protomodular)
reflective subcategory of $\mathcal{S}$-special objects of a Barr-exact
$\mathcal{S}$-protomodular category $\mathbb{C}$, where $\mathcal{S}$ is the class of
split epimorphic trivial extensions in $\mathbb{C}$. Next to some
concrete examples where the criterion may be applied, we also
study the adjunction between a Barr-exact unital category and its
abelian core, which we prove to be admissible.
Garner, Richard; Street, Ross
We give further insights into the weighted Hurwitz product and the
weighted tensor product of Joyal species. Our first group of results
relate the Hurwitz product to the pointwise product, including the
interaction with Rota--Baxter operators. Our second group of results
explain the first in terms of convolution with suitable bialgebras,
and show that these bialgebras are in fact obtained in a
particularly straightforward way by freely generating from pointed
coalgebras. Our third group of results extend this from linear
algebra to two-dimensional linear algebra, deriving the existence of
weighted Hurwitz monoidal structures on the category of species
using convolution with freely generated bimonoidales. Our final
group of results relate Hurwitz...
Clais, Antoine
We study the buildings in which parallelism of residues is an equivalence relation. If the building admits a group action, we describe how parallel residues are related to residues with equal stabilizers. This permits to retrieve the fact that in a Coxeter group or in a graph product, intersections of parabolic subgroups are parabolic.
Jiménez-Rodríguez, P.; Maghsoudi, S.; Muñoz-Fernández, G.A.; Seoane-Sepúlveda, J.B.
It is known that there is not a two dimensional linear space in $\mathbb R^\mathbb R$ every non-zero element of which is an injective function. Here, we generalize this result to arbitrarily large dimensions. We also study the convolution of non-differentiable functions which gives, as a result, a differentiable function. In this latter case, we are able to show the existence of linear spaces of the largest possible dimension formed by functions enjoying the previous property. By doing this we provide both positive and negative results to the recent field of lineability. Some open questions are also provided.
Amiri, S.; Golbaharan, A.; Mahyar, H.
Let $X$ be a perfect compact plane set, $n\in \mathbb{N}$ and $D^n(X)$ be
the algebra of complex-valued functions on $X$ with continuous
$n$-th derivative. In this paper we study weighted composition
operators on algebras $D^n(X)$. We give a necessary and sufficient
condition for these operators to be compact. As a consequence, we
characterize power compact composition operators on these
algebras. Then we determine the spectra of Riesz weighted
composition operators on these algebras.