Recursos de colección
Project Euclid (Hosted at Cornell University Library) (191.996 recursos)
Bulletin of the Belgian Mathematical Society-Simon Stevin
Bulletin of the Belgian Mathematical Society-Simon Stevin
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.
Jayanarayanan, C. R.; Rao, T. S. S. R. K.
In this paper, we study two optimization problems where solutions on a dense set yield global solution. We study these problems for spaces of Bochner integrable functions and for spaces of continuous functions.
The first one deals with expressing the length of a vector as a sum of the distance to a best approximation and minimal best approximation and the second one relates to approximating a subsequence of a minimizing sequence with a sequence of proximinal vectors.
Mahdavi, Ali; Rahmati, Farhad
We give a formula for a Frobenius vector of a Gorenstein simplicial affine semigroup $S$, and when the semigroup is Cohen-Macaulay we give an algorithm computing the set of minimal Frobenius vectors of $S$ for a special class of semigroups.
Liang, Hongxue; Zhou, Shenglin
We prove that if $\mathcal{D}$ is a non-trivial non-symmetric $2$-$(v,k,2)$ design
admitting a flag-transitive point-primitive automorphism group $G$ with $Soc(G)=A_{n}$ for $n\geq5$,
then $\mathcal{D}$ is a $2$-$(6,3,2)$ or $2$-$(10,4,2)$ design.
Nasr-Isfahani, Rasoul; Shahmoradi, Somayeh; Soltani Renani, Sima
For a Banach algebra ${\cal A}$, we introduce and investigate weak amenability of ${\cal A}$
with respect to a character. We give some necessary conditions for the weak
amenability of $\cal A$ with respect to a character and describe a class of Banach
algebras that are not weakly amenable with respect to characters.
Finally, we give examples of Banach algebras which are
weakly amenable with respect to characters but neither weakly amenable nor amenable
with respect to characters.
Salame, Khadime
In this paper we study common fixed point properties of non-linear actions of semi-topological semigroups on non-void weak* compact convex sets in dual Banach spaces. Among other things, we derive from our main result Theorem 1, the existence of a common fixed point property for semigroups of non-expansive mappings acting on non-empty weakly compact convex sets, generalizing a result of Hsu [13], Mitchell [25].
Khodaiemehr, Hossein; Sady, Fereshteh
In this paper we first investigate linear extendability of an
isometric embedding $T:\mathcal U \longrightarrow \mathcal Y$ from an open subset
$\mathcal U$ of a real Banach space $\mathcal X$ into a real Banach space $\mathcal Y$
in the case where $\mathcal Y$ is either the space $C_\Bbb R(K)$ of
continuous real-valued functions on a compact space $K$, or is a
strictly convex Banach space. Then we obtain similar results for
the case where $\mathcal Y$ is an arbitrary real Banach space and $T:\mathcal U
\longrightarrow \mathcal Y$ is an isometry whose range satisfies some
additional conditions.
Lourenço, Mary Lilian; Vieira, Daniela M.
We show that the subset of the disk algebra of the functions that are not in some Dales-Davie algebra is algebrable. In other words, the set $\Big\{f\in\mathcal{A}(D)\,:\,\sum_{n=0}^{\infty}\dfrac{\|f^{(n)}\|}{n!}=+\infty\Big\}$ is shown to be algebrable.
Zireh, Ahmad; Analouei Adegani, E.; Bulut, Serap
In this paper, we find coefficient estimates by a new method making use of
the Faber polynomial expansions for a comprehensive subclass of
analytic bi-univalent functions, which is defined by subordinations
in the open unit disk. The coefficient bounds presented in this
paper would generalize and improve some recent works appeared in the
literature.
Sebag, Julien
We introduce the notion of \emph{primitive arc} of a curve defined over a field $k$ and study criterions for the existence of such objects in terms of the geometry of the curve. We prove that this notion provides a criterion which determines when the normalization of an irreductible curve singularity $(X,x)$ induces an isomorphism between the formal neighborhoods of the associated arc schemes at the constant arc $x$ and its lifting $\bar x$ to the normalization $\bar X$. We also show that the existence of a primitive arc at $x\in X$ is equivalent to the smoothness of the analytically irreducible...