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1.
In his 1996 work developing the theory of association schemes as a generalized group theory, Zieschang introduced the concept of the semidirect product as a possible product operation of certain association schemes. In this paper we extend the semidirect product operation into the entire set of association schemes. We then derive a way to decompose certain association schemes into smaller association schemes. We also investigate to what extent this product helps us to understand and characterize the structure of association schemes. We give some examples to show that the semidirect product produces many schemes that cannot be described as neither the direct product nor the wreath product of smaller schemes.This research was supported by Com2MaC-KOSEF, Korea. 相似文献
2.
Sung Y. Song 《Journal of Algebraic Combinatorics》1996,5(1):47-55
If a symmetric association scheme of class two is realized as the symmetrization of a commutative association scheme, then it either admits a unique symmetrizable fission scheme of class three or four, or admits three fission schemes, two of which are class three and one is of class four. We investigate the classification problem for symmetrizable (commutative) association schemes of two-class symmetric association schemes. In particular, we give a classification of association schemes whose symmetrizations are obtained from completely multipartite strongly regular graphs in the notion of wreath product of two schemes. Also the cyclotomic schemes associated to Paley graphs and their symmetrizable fission schemes are discussed in terms of their character tables. 相似文献
3.
4.
Robert W. Baddeley 《Journal of Algebraic Combinatorics》1993,2(3):215-237
The paper addresses a part of the problem of classifying all 2-arc transitive graphs: namely, that of finding all groups acting 2-arc transitively on finite connected graphs such that there exists a minimal normal subgroup that is nonabelian and regular on vertices. A construction is given for such groups, together with the associated graphs, in terms of the following ingredients: a nonabelian simple group T, a permutation group P acting 2-transitively on a set , and a map F : Tsuch that x = x
–1 for all x
F() and such that Tis generated by F(). Conversely we show that all such groups and graphs arise in this way. Necessary and sufficient conditions are found for the construction to yield groups that are permutation equivalent in their action on the vertices of the associated graphs (which are consequently isomorphic). The different types of groups arising are discussed and various examples given. 相似文献
5.
John Panagopoulos 《Algebra Colloquium》2000,7(3):275-280
A group is called semicomplete if every automorphism which induces the identity on the factor commutator group is inner. In this paper, we study the connection of the semicompleteness of the permutational wreath product W of two groups with the semicompleteness of these groups. We give necessary conditions under which the group W is semicomplete.2000 Mathematics Subject Classification: 20E22, 20E36 相似文献
6.
给出了两个幺半群的半直积及圈积为右(左)逆半群的充分必要条件,从而推广了[2]中两个幺半群的半幺直积和圈积为逆半群的充分必要条件. 相似文献
7.
Pham Huu Tiep 《Mathematische Nachrichten》1997,184(1):313-327
The notion of globally irreducible representations of finite groups was introduced by B.H. Gross, in order to explain new series of Euclidean lattices discovered recently by N. Elkies and T. Shioda using Mordell–Weil lattices of elliptic curves. It has been observed by R. Gow and Gross that irreducible Weil representations of certain finite classical groups lead to globally irreducible representations. In this paper we classify all globally irreducible representations coming from Weil representations of finite classical groups. 相似文献
8.
Computational Mathematics and Mathematical Physics - An algorithm for the computation of the complete set of primitive orthogonal idempotents of the centralizer ring of the permutation... 相似文献
9.
Pham Huu Tiep 《Geometriae Dedicata》1997,64(1):85-123
The notion of globally irreducible representations of finite groups has been introduced by B. H. Gross, in order to explain new series of Euclidean lattices discovered recently by N. Elkies and T. Shioda using Mordell--Weil lattices of elliptic curves. In this paper we first give a necessary condition for global irreducibility. Then we classify all globally irreducible representations of L
2(q) and 2B2(q), and of the majority of the 26 sporadic finite simple groups. We also exhibit one more globally irreducible representation, which is related to the Weil representation of degree (pn-1)/2 of the symplectic group Sp2n(p) (p 1 (mod 4) is a prime). As a consequence, we get a new series of even unimodular lattices of rank 2(pn–1). A summary of currently known globally irreducible representations is given. 相似文献
10.
Adam Woryna 《代数通讯》2013,41(3):1354-1361
We study profinite groups which are infinitely iterated wreath products W ∞ = …?C n 2 ?C n 1 of finite cyclic groups via combinatorial language of transducers. Namely, we provide a naturally defined automaton realization of the group W ∞ by an automaton over a changing alphabet. Our construction gives a characterization of these profinite groups as automaton groups, i.e. as groups generated by a single automaton. 相似文献
11.
It is shown that the topologically irreducible representationsof a normed algebra define a certain topological radical inthe same way that the strictly irreducible representations definethe Jacobson radical and that this radical can be strictly smallerthan the Jacobson radical. An abstract theory of topologicalradicals in topological algebras is developed and usedto relate this radical to the Baer radical (prime radical).The relations with topologically transitive representationsand standard representations in the sense of Meyer are alsoexplored. 1991 Mathematics Subject Classification: 46H15, 46H25,16Nxx. 相似文献
12.
Edwin R. Van Dam 《Journal of Algebraic Combinatorics》1999,10(1):69-107
We study (symmetric) three-class association schemes. The graphs with four distinct eigenvalues which are one of the relations of such a scheme are characterized. We also give an overview of most known constructions, and obtain necessary conditions for existence. A list of feasible parameter sets on at most 100 vertices is generated. 相似文献
13.
Clyde H. Schoolfield Jr. 《Journal of Theoretical Probability》2002,15(3):667-693
We bound the rate of convergence to uniformity for a certain random walk on the complete monomial groups GS
n
for any group G. Specifically, we determine that
n log n+
n log (|G|–1|) steps are both necessary and sufficient for 2 distance to become small. We also determine that
n log n steps are both necessary and sufficient for total variation distance to become small. These results provide rates of convergence for random walks on a number of groups of interest: the hyperoctahedral group 2S
n
, the generalized symmetric group
m
S
n
, and S
m
S
n
. In the special case of the hyperoctahedral group, our random walk exhibits the cutoff phenomenon. 相似文献
14.
Silvia Montarani 《Algebras and Representation Theory》2007,10(5):471-479
In this note we refine the methods of Etingof and Montarani (Represent. Theory, 9: 457–467, 2005) in order to extend the main result of that article to a wider class of finite dimensional representations of wreath product
symplectic reflection algebras.
Presented by Claus M. Ringel. 相似文献
15.
TheNumbersofPermutationGroupsOrbitsandoftheWreathProductOrbits¥LiXianzhong;LiuGuangliang(PuyangEducationalCollege,Henan,45700... 相似文献
16.
A. V. Kosyak 《Functional Analysis and Its Applications》2004,38(1):67-68
Unitary representations of the group
are constructed. The construction uses G-quasi-invariant measures on some G-spaces that are subspaces of the space
of two-way infinite real matrices. We give a criterion for the irreducibility of these representations. 相似文献
17.
Kelly Wieand 《Journal of Theoretical Probability》2003,16(3):599-623
We consider a class of random matrix ensembles which can be constructed from the random permutation matrices by replacing the nonzero entries of the n×n permutation matrix matrix with M×M diagonal matrices whose entries are random Kth roots of unity or random points on the unit circle. Let X be the number of eigenvalues lying in a specified arc I of the unit circle, and consider the standardized random variable (X–E[X])/(Var(X))1/2. We show that for a fixed set of arcs I
1,...,I
N
, the corresponding standardized random variables are jointly normal in the large n limit, and compare the covariance structures which arise with results for other random matrix ensembles. 相似文献
18.
Julien Bichon 《Algebras and Representation Theory》2004,7(4):343-362
Let A be a compact quantum group, let nN
* and let A
aut(X
n
) be the quantum permutation group on n letters. A free wreath product construction A*w
A
aut(X
n
) is introduced. This construction provides new examples of quantum groups, and is useful to describe the quantum automorphism group of the n-times disjoint union of a finite connected graph. 相似文献
19.
We prove that the irreducible representations are finite-dimensional of the almost solvable restricted Lie algebras with the ascending chain condition for p-subalgebras over a perfect field. 相似文献
20.