共查询到20条相似文献,搜索用时 31 毫秒
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2.
作为拟三角弱Hopf代数的推广,我们引入了半拟三角弱Hopf代数的概念.令(H,R,v)是一个半拟三角弱Hopf代数,其中,R是其半拟三角结构.我们指明R保持了拟三角弱Hopf代数中泛R-矩阵的许多基本性质.特别地,讨论了Drinfeld元的性质,证明其是可逆的并且是余作用v的余不变量.另外,证明了半拟三角弱Hopf代数的对极平方是对合的. 相似文献
3.
Thomas Vetterlein 《Algebra Universalis》2008,58(2):129-143
Weak effect algebras are based on a commutative, associative and cancellative partial addition; they are moreover endowed
with a partial order which is compatible with the addition, but in general not determined by it. Every BL-algebra, i.e. the
Lindenbaum algebra of a theory of Basic Logic, gives rise to a weak effect algebra; to this end, the monoidal operation is
restricted to a partial cancellative operation.
We examine in this paper BL-effect algebras, a subclass of the weak effect algebras which properly contains all weak effect
algebras arising from BL-algebras. We describe the structure of BL-effect algebras in detail. We thus generalise the well-known
structure theory of BL-algebras.
Namely, we show that BL-effect algebras are subdirect products of linearly ordered ones and that linearly ordered BL-effect
algebras are ordinal sums of generalised effect algebras. The latter are representable by means of linearly ordered groups.
This research was partially supported by the German Science Foundation (DFG) as part of the Collaborative Research Center
“Computational Intelligence” (SFB 531). 相似文献
4.
Ivan Chajda 《Mathematica Slovaca》2010,60(1):21-32
Having an MV-algebra, we can restrict its binary operation addition only to the pairs of orthogonal elements. The resulting
structure is known as an effect algebra, precisely distributive lattice effect algebra. Basic algebras were introduced as
a generalization of MV-algebras. Hence, there is a natural question what an effect-like algebra can be reached by the above
mentioned construction if an MV-algebra is replaced by a basic algebra. This is answered in the paper and properties of these
effect-like algebras are studied. 相似文献
5.
The aim of this paper is to present several techniques of constructing a lattice-ordered effect algebra from a given family of lattice-ordered effect algebras, and to study the structure of finite lattice-ordered effect algebras. Firstly, we prove that any finite MV-effect algebra can be obtained by substituting the atoms of some Boolean algebra by linear MV-effect algebras. Then some conditions which can guarantee that the pasting of a family of effect algebras is an effect algebra are provided. At last, we prove that any finite lattice-ordered effect algebra E without atoms of type 2 can be obtained by substituting the atoms of some orthomodular lattice by linear MV-effect algebras. Furthermore, we give a way how to paste a lattice-ordered effect algebra from the family of MV-effect algebras. 相似文献
6.
The motivation of this paper is to study the natural quiver of an artinian algebra, a new kind of quivers, as a tool independing
upon the associated basic algebra. In Li (J Aust Math Soc 83:385–416, 2007), the notion of the natural quiver of an artinian algebra was introduced and then was used to generalize the Gabriel theorem
for non-basic artinian algebras splitting over radicals and non-basic finite dimensional algebras with 2-nilpotent radicals
via pseudo path algebras and generalized path algebras respectively. In this paper, firstly we consider the relationship between
the natural quiver and the ordinary quiver of a finite dimensional algebra. Secondly, the generalized Gabriel theorem is obtained
for radical-graded artinian algebras. Moreover, Gabriel-type algebras are introduced to outline those artinian algebras satisfying
the generalized Gabriel theorem here and in Li (J Aust Math Soc 83:385–416, 2007). For such algebras, the uniqueness of the related generalized path algebra and quiver holds up to isomorphism in the case
when the ideal is admissible. For an artinian algebra, there are two basic algebras, the first is that associated to the algebra
itself; the second is that associated to the correspondent generalized path algebra. In the final part, it is shown that for
a Gabriel-type artinian algebra, the first basic algebra is a quotient of the second basic algebra. In the end, we give an
example of a skew group algebra in which the relation between the natural quiver and the ordinary quiver is discussed. 相似文献
7.
本文研究了在Hom-Hopf代数上引入Hom-弱Hop代数的问题.通过建立弱左H-模Hom-代数的方法,构造Hom-smash积,证明Hom-smash积是Hom-代数,且给出使之成为Hom-弱Hopf代数的充分条件,推广了由Bohm等人定义的弱Hop代数. 相似文献
8.
本文研究了在Hom-Hopf代数上引入Hom-弱Hopf代数的问题.利用建立弱左H-Hom-余模双代数的方法,获得了Hom-smash余积的代数结构,并证明了Hom-smash余积是Hom-余代数和Hom-弱Hopf代数,推广了由Molnar定义的smash余积Hopf代数. 相似文献
9.
ALONSO LVAREZ Jos Nicanor FERNNDEZ VILABOA Jos Manuel GONZLEZ RODRíIGUEZ Ramón SONEIRA CALVO Carlos 《中国科学 数学(英文版)》2011,(5)
In this paper we study the projections of weak braided Hopf algebras using the notion of Yetter-Drinfeld module associated with a weak braided Hopf algebra. As a consequence, we complete the study ofthe structure of weak Hopf algebras with a projection in a braiding setting obtaining a categorical equivalencebetween the category of weak Hopf algebra projections associated with a weak Hopf algebra H living in abraided monoidal category and the category of Hopf algebras in the non-strict braided monoidal cate... 相似文献
10.
《数学年刊B辑(英文版)》2015,(6)
The aim of this paper is to investigate the first Hochschild cohomology of admissible algebras which can be regarded as a generalization of basic algebras.For this purpose,the authors study differential operators on an admissible algebra.Firstly,differential operators from a path algebra to its quotient algebra as an admissible algebra are discussed.Based on this discussion,the first cohomology with admissible algebras as coefficient modules is characterized,including their dimension formula.Besides,for planar quivers,the fc-linear bases of the first cohomology of acyclic complete monomial algebras and acyclic truncated quiver algebras are constructed over the field fc of characteristic 0. 相似文献
11.
We study the weak module amenability of Banach algebras which are
Banach module over another Banach algebra with compatible actions.
As an example we show that the semigroup algebra of a commutative inverse
semigroup is always weakly amenable as a module over the semigroup
algebra of its subsemigroup of idempotents. 相似文献
12.
The aim of this paper is to investigate the first Hochschild
cohomology of admissible algebras which can be regarded as a
generalization of basic algebras. For this purpose, the authors
study differential operators on an admissible algebra. Firstly,
differential operators from a path algebra to its quotient algebra
as an admissible algebra are discussed. Based on this discussion,
the first cohomology with admissible algebras as coefficient modules
is characterized, including their dimension formula. Besides, for
planar quivers, the $k$-linear bases of the first cohomology of
acyclic complete monomial algebras and acyclic truncated quiver
algebras are constructed over the field $k$ of characteristic $0$. 相似文献
13.
Zhi-xiang Wu 《高校应用数学学报(英文版)》2018,33(1):107-126
In this paper, we study a Yetter-Drinfeld module V over a weak Hopf algebra H.Although the category of all left H-modules is not a braided tensor category, we can define a Yetter-Drinfeld module. Using this Yetter-Drinfeld modules V, we construct Nichols algebra B(V) over the weak Hopf algebra H, and a series of weak Hopf algebras. Some results of [8] are generalized. 相似文献
14.
H. Vernaeve 《Monatshefte für Mathematik》2003,80(2):307-318
It is a known open question whether in Rosinger’s nowhere dense quotient algebra distributions can be embedded, ensuring consistency with partial derivatives. In this paper, we construct algebras of generalized functions with nowhere dense singularities similar to Rosinger’s algebra in which such an embedding of distributions is possible. Moreover, in some of the algebras, the embedding preserves the products of smooth functions. Further, we indicate that most of the properties of Rosinger’s algebra, in particular concerning the solvability of nonlinear PDEs, remain valid in the new algebras. Summarizing, we give a positive answer to the above-mentioned open question, if one allows a modification in the definition of the algebra that does not affect its basic properties. 相似文献
15.
H. Vernaeve 《Monatshefte für Mathematik》2003,138(4):307-318
It is a known open question whether in Rosinger’s nowhere dense quotient algebra distributions can be embedded, ensuring
consistency with partial derivatives. In this paper, we construct algebras of generalized functions with nowhere dense singularities
similar to Rosinger’s algebra in which such an embedding of distributions is possible. Moreover, in some of the algebras,
the embedding preserves the products of smooth functions. Further, we indicate that most of the properties of Rosinger’s algebra,
in particular concerning the solvability of nonlinear PDEs, remain valid in the new algebras. Summarizing, we give a positive
answer to the above-mentioned open question, if one allows a modification in the definition of the algebra that does not affect
its basic properties.
Received September 20, 2001; in final form April 11, 2002 相似文献
16.
R. Hazrat 《Israel Journal of Mathematics》2013,195(2):833-895
A Leavitt path algebra associates to a directed graph a ?-graded algebra and in its simplest form it recovers the Leavitt algebra L(1, k). In this note, we first study this ?-grading and characterize the (?-graded) structure of Leavitt path algebras, associated to finite acyclic graphs, C n -comet, multi-headed graphs and a mixture of these graphs (i.e., polycephaly graphs). The last two types are examples of graphs whose Leavitt path algebras are strongly graded. We give a criterion when a Leavitt path algebra is strongly graded and in particular characterize unital Leavitt path algebras which are strongly graded completely, along the way obtaining classes of algebras which are group rings or crossed-products. In an attempt to generalize the grading, we introduce weighted Leavitt path algebras associated to directed weighted graphs which have natural ⊕?-grading and in their simplest form recover the Leavitt algebras L(n, k). We then show that the basic properties of Leavitt path algebras can be naturally carried over to weighted Leavitt path algebras. 相似文献
17.
Ivan Chajda 《Order》2009,26(2):149-162
To any bounded lattice with section antitone bijections can be assigned an algebra with two binary, two unary and a nullary
operations satisfying similar axioms as a basic algebra. Due to the doubled similarity type, this algebra is called a double
basic algebra. Also conversely, every double basic algebra induces a bounded lattice equipped with antitone bijections in
every section. We study properties of double basic algebras, their interval algebras and several conclusions of the so-called
pseudo-commutativity.
This work is supported by the Research Project MSM 6198959214 by Czech Government. 相似文献
18.
Certain operator algebras A on a Hilbert space have the property that every densely defined linear transformation commuting with A is closable. Such algebras are said to have the closability property. They are important in the study of the transitive algebra problem. More precisely, if A is a two-transitive algebra with the closability property, then A is dense in the algebra of all bounded operators, in the weak operator topology. In this paper we focus on algebras generated by a completely nonunitary contraction, and produce several new classes of algebras with the closability property. We show that this property follows from a certain strict cyclicity property, and we give very detailed information on the class of completely nonunitary contractions satisfying this property, as well as a stronger property which we call confluence. 相似文献
19.
弱Hopf代数作用与冲积 总被引:1,自引:0,他引:1
本文研究了弱Hopf代数上的冲积并讨论了它约性质.设H是弱Hopf代数,A是左H-摸代数.我们给出了冲积A#H是弱双代数的一个充分条件以及A#H是A可分扩张的一个判定条件.另外,利用积分理论研究了Hopf模代数的有限性条件. 相似文献
20.
Ralph Stöhr 《Journal of Pure and Applied Algebra》2008,212(5):1187-1206
We use the technique known as elimination to devise some new bases of the free Lie algebra which (like classical Hall bases) consist of Lie products of left normed basic Lie monomials. Our bases yield direct decompositions of the homogeneous components of the free Lie algebra with direct summands that are particularly easy to describe: they are tensor products of metabelian Lie powers. They also give rise to new filtrations and decompositions of free Lie algebras as modules for groups of graded algebra automorphisms. In particular, we obtain some new decompositions for free Lie algebras and free restricted Lie algebras over fields of positive characteristic. 相似文献