共查询到20条相似文献,搜索用时 671 毫秒
1.
F. Bergeron N. Bergeron R.B. Howlett D.E. Taylor 《Journal of Algebraic Combinatorics》1992,1(1):23-44
The purpose of this paper is twofold. First we aim to unify previous work by the first two authors, A. Garsia, and C. Reutenauer (see [2], [3], [4], [5] and [10]) on the structure of the descent algebras of the Coxeter groups of type A
n and B
n. But we shall also extend these results to the descent algebra of an arbitrary finite Coxeter group W. The descent algebra, introduced by Solomon in [14], is a subalgebra of the group algebra of W. It is closely related to the subring of the Burnside ring B(W) spanned by the permutation representations W/W
J, where the W
J are the parabolic subgroups of W. Specifically, our purpose is to lift a basis of primitive idempotents of the parabolic Burnside algebra to a basis of idempotents of the descent algebra. 相似文献
2.
In this paper, we study a tower {A
n
G: n} ≥ 1 of finite-dimensional algebras; here, G represents an arbitrary finite group,d denotes a complex parameter, and the algebraA
n
G(d) has a basis indexed by ‘G-stable equivalence relations’ on a set whereG acts freely and has 2n orbits. We show that the algebraA
n
G(d) is semi-simple for all but a finite set of values ofd, and determine the representation theory (or, equivalently, the decomposition into simple summands) of this algebra in the
‘generic case’. Finally we determine the Bratteli diagram of the tower {A
n
G(d): n} ≥ 1 (in the generic case). 相似文献
3.
In this paper we define the hyper operations ?, ∨ and ∧ on a hyper MV ‐algebra and we obtain some related results. After that by considering the notions ofhyper MV ‐ideals and weak hyper MV ‐ideals, we prove some theorems. Then we determine relationships between (weak) hyper MV ‐ideals in a hyper MV ‐algebra (M, ⊕, *, 0) and (weak) hyper K ‐ideals in a hyper K ‐algebra (M, °, 0). Finally we give a characterization of hyper MV ‐algebras of order 3 or 4 based on the (weak) hyper MV ‐ideals (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
4.
5.
Kaiming Zhao 《数学学报(英文版)》1999,15(2):145-152
In this paper, automorphisms of the algebra ofq-difference operators, as an associative algebra for arbitraryq and as a Lie algebra forq being not a root of unity, are determined.
Project supported by the NNSF of China 相似文献
6.
Anatolij Dvurečenskij 《Czechoslovak Mathematical Journal》2006,56(1):47-59
We give two variations of the Holland representation theorem for ℓ-groups and of its generalization of Glass for directed
interpolation po-groups as groups of automorphisms of a linearly ordered set or of an antilattice, respectively. We show that
every pseudo-effect algebra with some kind of the Riesz decomposition property as well as any pseudo MV-algebra can be represented as a pseudo-effect algebra or as a pseudo MV-algebra of automorphisms of some antilattice or of some linearly ordered set. 相似文献
7.
The aim of the present paper is to define the localization MV-algebra of an
MV-algebra A with respect to a topology
on A; also, following the categorical equivalence
between the category of lu-groups and the category of
MV-algebras, we define the analogous
notion for lu-groups. In Section 5 we prove that the maximal
MV-algebra of quotients
(defined in [7]) and the MV-algebra of fractions relative to an -closed
system (defined in [6]) are MV-algebras of localization.In the last part of this paper (Section 6) we prove analogous results for lu-groups. 相似文献
8.
The max algebra consists of the nonnegative real numbers equipped with two binary operations, maximization and multiplication. We characterize
the invertible linear operators that preserve the set of commuting pairs of matrices over a subalgebra of max algebra. 相似文献
9.
V. V. Zharinov 《Theoretical and Mathematical Physics》1999,118(2):129-151
Derivations of the Heisenberg algebraH and some related questions are studied. The ideas and the language of formal differential geometry are used. It is proved
that all derivations of this algebra are inner. The main subalgebras of the Lie algebraD(H) of all derivations ofH are distinguished, and their properties are studied. It is shown that the algebraH interpreted as a Lie algebra (with the commutator as the Lie bracket) forms a one-dimensional central extension ofD(H).
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 118. No. 2 pp. 163–189, February, 1999. 相似文献
10.
Somayeh Motamed Lida Torkzadeh Arsham Borumand Saeid Neda Mohtashamnia 《Mathematical Logic Quarterly》2011,57(2):166-179
In this paper, the notion of the radical of a filter in BL‐algebras is defined and several characterizations of the radical of a filter are given. Also we prove that A/F is an MV‐algebra if and only if Ds(A) ? F. After that we define the notion of semi maximal filter in BL‐algebras and we state and prove some theorems which determine the relationship between this notion and the other types of filters of a BL‐algebra. Moreover, we prove that A/F is a semi simple BL‐algebra if and only if F is a semi maximal filter of A. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献
11.
J. Szenthe 《Central European Journal of Mathematics》2004,2(5):725-731
Spherically symmetric space-times have attained considerable attention ever since the early beginnings of the theory of general
relativity. In fact, they have appeared already in the papers of K. Schwarzschild [12] and W. De Sitter [5] which were published
in 1916 and 1917 respectively soon after Einstein's epoch-making work [7] in 1915. The present survey is concerned mainly
with recent results pertainig to the toplogy of spherically symmetric space-times.
Definition. By space-time a connected time-oriented 4-dimensional Lorentz manifold is meant. If (M,<,>) is a space-time, and Φ: SO(3)×M→M an isometric action such that the maximal dimension of its orbits is equal to 2, then the action Φ is said to be spherical and the space-time is said to be spherically symmetric [8]; [11]. Likewise, isometric actions Ψ: O(3)×M→M are also considered ([10], p. 365; [4]) which will be called quasi-spherical if the maximal dimension of its orbits is 2 and then the space-time is said to be quasi-spherically symmetric here. Each quasi-spherical action yields a spherical one by restricting it to the action of SO(3); the converse of this statement will be considered elsewhere.
The main results concerning spherically symmetric space-times are generally either of local character or pertaining to topologically
restricted simple situations [14], and earlier results of global character are scarce [1], [4], [6], [13]. A report on recent
results concerning the global geometry of spherically symmetric space-times [16] is presented below. 相似文献
12.
Ioannis Emmanouil 《K-Theory》2005,35(3-4):257-271
Let G be a group and k a subring of the field of complex numbers. In this paper we study the additive map in reduced K-theory, which is associated with the inclusion of the group algebra kG into the group von Neumann algebra
G, and obtain necessary and sufficient conditions for it to be identically zero (or zero modulo torsion). Our results complete
the work of Eckmann [Comm. Math. Helvet. 71 (1996), 453–462; Arch. Math. 76 (2001), 241–249] and Schafer [K-theory 19 (2000), 211–217], while reducing to Swan’s theorem on induced representations [Ann. Math. 71 (1960), 552–578], in the case where the group G is finite.
(Received: January 2005)
Research supported by University of Athens grant Pythagoras 70/3/7298. 相似文献
13.
Florentina Chirte§ 《Central European Journal of Mathematics》2005,3(1):105-124
The aim of this paper is to define the localization LM
n
-algebra of an LM
n
—algebra L with respect to a topology F on L; in Section 5 we prove that the maximal LM
n
-algebra of fractions (defined in [3]) and the LM
n
-algebra of fractions relative to an Λ—closed system (defined in Section 2) are LM
n
-algebras of localization. 相似文献
14.
Diming Lu 《中国科学A辑(英文版)》1998,41(2):139-146
Let (H,R) be a triangular Hopf algebra. The monoidal functors on the category of representations ofH is studied, and a universal quantum commutative algebraSeR(M) and a dual H°-comoduleM° for any H-moduleM with an integrale are constructed. Both constructions given here have tensor isomorphism properties.
Project supported by the National Natural Science Foundation of China. 相似文献
15.
16.
17.
Rafał Bocian Thorsten Holm Andrzej Skowroński 《Central European Journal of Mathematics》2004,2(1):67-75
Auslander’s representation dimension measures how far a finite dimensional algebra is away from being of finite representation
type. In [1], M. Auslander proved that a finite dimensional algebra A is of finite representation type if and only if the representation dimension of A is at most 2. Recently, R. Rouquier proved that there are finite dimensional algebras of an arbitrarily large finite representation
dimension. One of the exciting open problems is to show that all finite dimensional algebras of tame representation type have
representation dimension at most 3. We prove that this is true for all domestic weakly symmetric algebras over algebraically
closed fields having simply connected Galois coverings. 相似文献
18.
Jan Jakubik 《Czechoslovak Mathematical Journal》2001,51(3):609-616
Riecan [12] and Chovanec [1] investigated states in MV-algebras. Earlier, Riecan [11] had dealt with analogous ideas in D-posets. In the monograph of Riecan and Neubrunn [13] (Chapter 9) the notion of state is applied in the theory of probability on MV-algebras. We remark that a different definition of a state in an MV-algebra has been applied by Mundici [9], [10] (namely, the condition (iii) from Definition 1.1 above was not included in his definition of a state; in other words, only finite additivity was assumed). Below we work with the definition from [13]; but, in order to avoid terminological problems we use the term "state-homomorphism" (instead of "state"). The author is indebted to the referee for his suggestion concerning terminology. Let
be an MV-algebra which is defined on a set A with card A>1. In the present paper we show that there exists a one-to-one correspondence between the system of all state-homomorphisms on
and the system of all -closed maximal ideals of
. For MV-algebras we apply the notation and the definitions as in Gluschankof [3]. The relations between MV-algebras and abelian lattice ordered groups (cf. Mundici [8]) are substantially used in the present paper. 相似文献
19.
In analogy with effect algebras, we introduce the test spaces and MV-test spaces. A test corresponds to a hypothesis on the propositional system, or, equivalently, to a partition of unity. We show that there is a close correspondence between MV-algebras and MV-test spaces. 相似文献
20.
Savita Bhatnagar 《Proceedings Mathematical Sciences》2005,115(4):383-389
The aim of this paper is to study the algebraAC
p
of absolutely continuous functionsf on [0,1] satisfying f(0) = 0,f ’ ∈ Lp[0, 1] and the multipliers ofAC
p
. 相似文献