共查询到20条相似文献,搜索用时 234 毫秒
1.
A. Joseph Kennedy 《代数通讯》2013,41(1):145-170
In this article, we study an important subalgebra of the tensor product partition algebra P k (x)? P k (y), denoted by P k (x, y) and called “Class Partition Algebra.” We show that the algebra P k (n, m) is the centralizer algebra of the wreath product S m ? S n . Furthermore, the algebra P k (x, y) and the tensor product partition algebra P k (x)? P k (y) are subalgebras of the G-colored partition algebra P k (x;G) and G-vertex colored partition algebra P k (x, G) respectively, for every group G with |G|=y ≥ 2k. 相似文献
2.
Slobodan Tanushevski 《代数通讯》2013,41(10):4378-4410
For a given group G and a homomorphism ?: G → G × G, we construct groups ??(G), 𝒯?(G), and 𝒱?(G) that blend Thompson's groups F, T, and V with G, respectively. Furthermore, we describe the lattice of normal subgroups of the groups ?Δ(G), where Δ: G → G × G is the diagonal homomorphism, Δ(g) = (g, g). 相似文献
3.
We give a positive answer to the Berry-Robbins problem for any compact Lie group G, i.e. we show the existence of a smooth W-equivariant map from the space of regular triples in a Cartan subalgebra to the flag manifold G/T . This map is constructed via solutions to Nahm's equations and it is compatible with the S
O(3) action, where S
O(3) acts on G/T via a regular homomorphism from S
U(2) to G. We then generalize this picture to include an arbitrary homomorphism from S
U(2) to G. This leads to an interesting geometrical picture which appears to be related to the Springer representation of the Weyl
group and the work of Kazhdan and Lusztig on representations of Hecke algebras.
Received: 8 February 2002 相似文献
4.
George Szeto 《代数通讯》2013,41(12):3979-3985
Let B be a Galois algebra over a commutative ring R with Galois group G such that B H is a separable subalgebra of B for each subgroup H of G. Then it is shown that B satisfies the fundamental theorem if and only if B is one of the following three types: (1) B is an indecomposable commutative Galois algebra, (2) B = Re ⊕ R(1 ? e) where e and 1 ? e are minimal central idempotents in B, and (3) B is an indecomposable Galois algebra such that for each separable subalgebra A, V B (A) = ?∑ g∈G(A) J g , and the centers of A and B G(A) are the same where V B (A) is the commutator subring of A in B, J g = {b ∈ B | bx = g(x)b for each x ∈ B} for a g ∈ G, and G(A) = {g ∈ G | g(a) = a for all a ∈ A}. 相似文献
5.
M. H. Lim 《Linear and Multilinear Algebra》2013,61(4):333-354
Let G be a subgroup of the symmetric group Sm and V be an n-dimensional unitary space where nm. Let V(G) be the symmetry class of tensors over V associated with G and the identity character. Let D(G) be the set of all decomposable elements of V(G) and O(G) be its subset consisting of all nonzero decomposable tensors x 1 ?…? xm such that {x 1,…,xm } is an orthogonal set. In this paper we study the structure of linear mappings on V(G) that preserve one of the following subsets: (i)O(G), (ii) D(G)\(O(G)?{0}). 相似文献
6.
Under what conditions is it true that if there is a graph homomorphism G □ H → G □ T, then there is a graph homomorphism H→ T? Let G be a connected graph of odd girth 2k + 1. We say that G is (2k + 1)‐angulated if every two vertices of G are joined by a path each of whose edges lies on some (2k + 1)‐cycle. We call G strongly (2k + 1)‐angulated if every two vertices are connected by a sequence of (2k + 1)‐cycles with consecutive cycles sharing at least one edge. We prove that if G is strongly (2k + 1)‐angulated, H is any graph, S, T are graphs with odd girth at least 2k + 1, and ?: G□ H→S□T is a graph homomorphism, then either ? maps G□{h} to S□{th} for all h∈V(H) where th∈V(T) depends on h; or ? maps G□{h} to {sh}□ T for all h∈V(H) where sh∈V(S) depends on h. This theorem allows us to prove several sufficient conditions for a cancelation law of a graph homomorphism between two box products with a common factor. We conclude the article with some open questions. © 2008 Wiley Periodicals, Inc. J Graph Theory 58:221‐238, 2008 相似文献
7.
Let G be a graph and W a subset of V(G). Let g,f:V(G)→Z be two integer-valued functions such that g(x)≤f(x) for all x∈V(G) and g(y)≡f(y) (mod 2) for all y∈W. Then a spanning subgraph F of G is called a partial parity (g,f)-factor with respect to W if g(x)≤deg
F
(x)≤f(x) for all x∈V(G) and deg
F
(y)≡f(y) (mod 2) for all y∈W. We obtain a criterion for a graph G to have a partial parity (g,f)-factor with respect to W. Furthermore, by making use of this criterion, we give some necessary and sufficient conditions for a graph G to have a subgraph which covers W and has a certain given property.
Received: June 14, 1999?Final version received: August 21, 2000 相似文献
8.
P. P. Nikitin 《Journal of Mathematical Sciences》2007,141(4):1479-1493
We consider the walled Brauer algebra Br
k, l(n) introduced by V. Turaev and K. Koike. We prove that it is a subalgebra of the Brauer algebra and that it is isomorphic,
for sufficiently large n ∈ ℕ, to the centralizer algebra of the diagonal action of the group GLn(ℂ) in a mixed tensor space. We also give the presentation of the algebra Br
k, l(n) by generators and relations. For a generic value of the parameter, the algebra is semisimple, and in this case we describe
the Bratteli diagram for this family of algebras and give realizations for the irreducible representations. We also give a
new, more natural proof of the formulas for the characters of the walled Brauer algebras. Bibliography: 29 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 331, 2006, pp. 170–198. 相似文献
9.
《代数通讯》2013,41(11):5305-5318
Abstract Let 𝔤 be a complex semisimple Lie algebra with adjoint group G and let 𝔥 be a Cartan subalgebra of 𝔤. Let Â(𝔤) and Â(𝔥) denote the algebra of differential operators with formal power series coefficients on 𝔤 and 𝔥 respectively. We construct a subalgebra A 𝔤 of Â(𝔤) containing all the pull-backs of the differential operators in G attached to any element x in 𝔤. We also consider the projection P: A 𝔤 → Â 𝔥. Then, we calculate explicity the pull-back of the differential operator in G attached to an element h in 𝔥 modulo Ker P. 相似文献
10.
Jonathan Elmer 《Archiv der Mathematik》2008,91(6):481-485
Let G be a finite group acting linearly on a finite dimensional vector space V defined over a field k of characteristic p, where p is assumed to divide the group order. Let R := S(V *) be the symmetric algebra of the dual on which G acts naturally by algebra automorphisms. We study the RG-modules Hi(G, R) for i > 0. In particular we give a formula which describes the annihilator of a general element of Hi(G, R) in terms of the relative transfer ideals of RG, and consequently prove that the associated primes of these cohomology modules are equal to the radicals of certain relative
transfer ideals.
Received: 5 June 2008 相似文献
11.
Let G be a graph and f be a mapping from V(G) to the positive integers. A subgraph T of G is called an f‐tree if T forms a tree and dT(x)≤f(x) for any x∈V(T). We propose a conjecture on the existence of a spanning f‐tree, and give a partial solution to it. © 2009 Wiley Periodicals, Inc. J Graph Theory 65: 173–184, 2010 相似文献
12.
Given graphs G, H, and lists L(v) ? V(H), v ε V(G), a list homomorphism of G to H with respect to the lists L is a mapping f : V(G) → V(H) such that uv ε E(G) implies f(u)f(v) ε E(H), and f(v) ε L(v) for all v ε V(G). The list homomorphism problem for a fixed graph H asks whether or not an input graph G, together with lists L(v) ? V(H), v ε V(G), admits a list homomorphism with respect to L. In two earlier papers, we classified the complexity of the list homomorphism problem in two important special cases: When H is a reflexive graph (every vertex has a loop), the problem is polynomial time solvable if H is an interval graph, and is NP‐complete otherwise. When H is an irreflexive graph (no vertex has a loop), the problem is polynomial time solvable if H is bipartite and H is a circular arc graph, and is NP‐complete otherwise. In this paper, we extend these classifications to arbitrary graphs H (each vertex may or may not have a loop). We introduce a new class of graphs, called bi‐arc graphs, which contains both reflexive interval graphs (and no other reflexive graphs), and bipartite graphs with circular arc complements (and no other irreflexive graphs). We show that the problem is polynomial time solvable when H is a bi‐arc graph, and is NP‐complete otherwise. In the case when H is a tree (with loops allowed), we give a simpler algorithm based on a structural characterization. © 2002 Wiley Periodicals, Inc. J Graph Theory 42: 61–80, 2003 相似文献
13.
Volker Runde 《Monatshefte für Mathematik》1997,123(3):245-252
LetG be a Moore group, letB be a Banach algebra, and let :L
1(G)B be a homomorphism. We show that is continuous if and only if its restriction to the center ofL
1(G) is continuous. As a consequence, we obtain that (i) every homomorphism fromL
1(G) orC
*(G) onto a dense subalgebra of a semisimple Banach algebra, and (ii) every epimorphism fromC
*(G) onto a Banach algebra is automatically continuous. 相似文献
14.
Jaroslav Neetil 《Journal of Graph Theory》2002,39(2):108-110
A graph G is called rigid if the identical mapping V(G)→V(G) is the only homomorphism G→G. In this note we give a simple construction of a rigid oriented graph on every set. © 2002 John Wiley & Sons, Inc. J Graph Theory 39: 108–110, 2002 相似文献
15.
Götz Pfeiffer 《Advances in Mathematics》2009,220(5):1428-1465
The descent algebra Σ(W) is a subalgebra of the group algebra QW of a finite Coxeter group W, which supports a homomorphism with nilpotent kernel and commutative image in the character ring of W. Thus Σ(W) is a basic algebra, and as such it has a presentation as a quiver with relations. Here we construct Σ(W) as a quotient of a subalgebra of the path algebra of the Hasse diagram of the Boolean lattice of all subsets of S, the set of simple reflections in W. From this construction we obtain some general information about the quiver of Σ(W) and an algorithm for the construction of a quiver presentation for the descent algebra Σ(W) of any given finite Coxeter group W. 相似文献
16.
A. M. H. Gerards 《Journal of Graph Theory》1988,12(1):73-83
We give a class of graphs G for which there exists a homomorphism (= adjacency preserving map) from V(G) to V(C), where C is the shortest odd cycle in G, thereby extending a result of Albertson, Catlin, and Gibbons. Our class of graphs is characterized by the following property: For each odd subdivision G′ of G there exists a homomorphic map from V(G′) to V(C), where C′ is the shortest odd cycle of G′. 相似文献
17.
Bart de Bruyn 《Linear and Multilinear Algebra》2013,61(7):887-902
Let V be 2n-dimensional vector space over a field 𝕂 equipped with a nondegenerate skew-ψ-Hermitian form f of Witt index n ≥ 1, let 𝕂0 ? 𝕂 be the fix field of ψ and let G denote the group of isometries of (V, f). For every k ∈ {1, …, 2n}, there exist natural representations of the groups G ? U(2n, 𝕂/𝕂0) and H = G ∩ SL(V) ? SU(2n, 𝕂/𝕂0) on the k-th exterior power of V. With the aid of linear algebra, we prove some properties of these representations. We also discuss some applications to projective embeddings and hyperplanes of Hermitian dual polar spaces. 相似文献
18.
Let G be a group and ?:H→G be a contracting homomorphism from a subgroup H<G of finite index. V. Nekrashevych (2005) [25] associated with the pair (G,?) the limit dynamical system (JG,s) and the limit G-space XG together with the covering ?g∈GT⋅g by the tile T. We develop the theory of self-similar measures m on these limit spaces. It is shown that (JG,s,m) is conjugated to the one-sided Bernoulli shift. Using sofic subshifts we prove that the tile T has integer measure and we give an algorithmic way to compute it. In addition we give an algorithm to find the measure of the intersection of tiles T∩(T⋅g) for g∈G. We present applications to the invariant measures for the rational functions on the Riemann sphere and to the evaluation of the Lebesgue measure of integral self-affine tiles. 相似文献
19.
Baogang Xu 《Journal of Graph Theory》1998,29(3):133-137
The total chromatic number χT(G) of graph G is the least number of colors assigned to V(G) ∪ E(G) such that no adjacent or incident elements receive the same color. In this article, we give a sufficient condition for a bipartite graph G to have χT(G) = Δ(G) + 1. © 1998 John Wiley & Sons, Inc. J. Graph Theory 29: 133–137, 1998 相似文献
20.
Let (X, F) be an Alexandroff space, let A(F) be the Boolean subalgebra of 2
X
generated by F, let G be a Hausdorff commutative topological lattice group and let rbaF(A(F), G) denote the set of all order bounded F-inner regular finitely additive set functions from A(F) into G. Using some special properties of the elements of rbaF(A(F), G), we extend to this setting the first decomposition theorem of Alexandroff. 相似文献