共查询到20条相似文献,搜索用时 46 毫秒
1.
Let H 2 be Sweedler’s 4-dimensional Hopf algebra and r(H 2) be the corresponding Green ring of H 2. In this paper, we investigate the automorphism groups of Green ring r(H 2) and Green algebra F(H 2) = r(H 2)?? F, where F is a field, whose characteristics is not equal to 2. We prove that the automorphism group of r(H 2) is isomorphic to K 4, where K 4 is the Klein group, and the automorphism group of F(H 2) is the semidirect product of ?2 and G, where G = F {1/2} with multiplication given by a · b = 1? a ? b + 2ab. 相似文献
2.
3.
Sun Haina Bu Yuehua 《高校应用数学学报(英文版)》2006,21(4):487-492
The relations among the dominating number, independence number and covering number of hypergraphs are investigated. Main results are as follows:Dv(H)≤min{α≤(H), p(H), p(H), T(H)}; De(H)≤min{v(H), T(H), p(H)}; DT(H) ≤αT(H); S(H)≤ Dv (H) + α(H)≤n; 2≤ Dv (H) + T(H) ≤n; 2 〈 Dv (H) + v(H)≤n/2 + [n/r]; Dv (H) + p(H) 〈_n;2≤De(H) + Dv(H)≤n/2 + [n/r];α(H) + De(H)≤n;2 ≤ De(H) + v(H)≤2[n/r]; 2 De(H) + p(H)≤n-r + 2. 相似文献
4.
Dong Yang 《Algebras and Representation Theory》2007,10(6):619-629
Let A be a finitary algebra over a finite field k, and A-
\textmod\text{mod} the category of finite dimensional left A-modules. Let H(A)\mathcal{H}(A) be the corresponding Hall algebra, and for a positive integer r let D
r
(A) be the subspace of H(A)\mathcal{H}(A) which has a basis consisting of isomorphism classes of modules in A-
\textmod\text{mod} with at least r + 1 indecomposable direct summands. If A is the path algebra of the quiver of type A
n
with linear orientation, then D
r
(A) is known to be the kernel of the map from the twisted Hall algebra to the quantized Schur algebra indexed by n + 1 and r. For any A, we determine necessary and sufficient conditions for D
r
(A) to be an ideal and some conditions for D
r
(A) to be a subring of H(A)\mathcal{H}(A). For A the path algebra of a quiver, we also determine necessary and sufficient conditions for D
r
(A) to be a subring of H(A)\mathcal{H}(A). 相似文献
5.
F. E. A. Johnson 《代数通讯》2013,41(5):2034-2047
Let G be a finite group with integral group ring Λ =Z[G]. The syzygies Ωr(Z) are the stable classes of the intermediate modules in a free Λ-resolution of the trivial module. They are of significance in the cohomology theory of G via the “co-represention theorem” Hr(G, N) = Hom𝒟er(Ωr(Z), N). We describe the Ωr(Z) explicitly for the dihedral groups D4n+2, so allowing the construction of free resolutions whose differentials are diagonal matrices over Λ. 相似文献
6.
Jie Du 《manuscripta mathematica》1992,75(1):411-427
The structure of Schur algebrasS(2,r) over the integral domainZ is intensively studied from the quasi-hereditary algebra point of view. We introduce certain new bases forS(2,r) and show that the Schur algebraS(2,r) modulo any ideal in the defining sequence is still such a Schur algebra of lower degree inr. A Wedderburn-Artin decomposition ofS
K
(2,r) over a fieldK of characteristic 0 is described. Finally, we investigate the extension groups between two Weyl modules and classify the
indecomposable Weyl-filtered modules for the Schur algebrasS
Zp(2,r) withr<p
2
.
Research supported by ARC Large Grant L20.24210 相似文献
7.
Hisashi Matsuyama Toshikatsu Koga 《Journal of Computational and Applied Mathematics》2010,233(6):1584-1589
The one-electron radial density function D(r) has recently been found to be separable into inner D<(r) and outer D>(r) radial density functions. The inner D<(r) and outer D>(r) densities are studied for 28 singly-excited 1snl singlet and triplet states (0≤l<n≤5) of the He atom at a correlated level. Theoretical structures of D<(r) and D>(r) are discussed within the Hartree-Fock framework. Comparison of correlated D<(r) and D>(r) with hydrogenic radial densities based on the modal characteristics and Carbó’s similarity index clarifies that D<(r) represents the 1s density of the helium cation, while D>(r) extracts the nl density of the hydrogen atom from D(r). The radial separation 〈|r1−r2|〉, which constitutes a lower bound to the standard deviation of D(r), is shown to be estimated from the location of the outermost maximum of D>(r). 相似文献
8.
Janko Marovt 《Linear algebra and its applications》2010,432(6):1595-1607
Let D be an arbitrary division ring and Mn(D) the multiplicative semigroup of all n×n matrices over D. We study non-degenerate, injective homomorphisms from M2(D) to M4(D). In particular, we present a structural result for the case when D is the ring of quaternions. 相似文献
9.
Let k be a field and A n (ω) be the Taft's n 2-dimensional Hopf algebras. When n is odd, the Drinfeld quantum double D(A n (ω)) of A n (ω) is a Ribbon Hopf algebra. In the previous articles, we constructed an n 4-dimensional Hopf algebra H n (p, q) which is isomorphic to D(A n (ω)) if p ≠ 0 and q = ω?1, and studied the finite dimensional representations of H n (1, q). We showed that the basic algebra of any nonsimple block of H n (1, q) is independent of n. In this article, we examine the infinite representations of H 2(1, ? 1), or equivalently of H n (1, q)?D(A n (ω)) for any n ≥ 2. We investigate the indecomposable and algebraically compact modules over H 2(1, ? 1), describe the structures of these modules and classify them under the elementary equivalence. 相似文献
10.
Yasuhiro Gotoh 《Journal d'Analyse Mathématique》2000,82(1):149-173
For a given growth functionH, we say that a domainD ?R n is anH-domain if δD x≤δD(x 0)H(k D(x,x 0)),x ∈D, where δD(x)=d(x?D) andk D denotes the quasihyperbolic distance. We show that ifH satisfiesH(0)=1, |H'|≤H, andH"≤H, then there exists an extremalH-domain. Using this fact, we investigate some fundamental properties ofH-domains. 相似文献
11.
Let M be a finitely generated torsion-free module over a one-dimensional reduced Noetherian ring R with finitely generated normalization. The rank of M is the tuple of vector-space dimensions of MP over each field RP (R localized at P), where P ranges over the minimal prime ideals of R. We assume that there exists a bound NR on the ranks of all indecomposable finitely generated torsion-free R-modules. For such rings, what bounds and ranks occur? Partial answers to this question have been given by a plethora of authors over the past forty years. In this article we provide a final answer by giving a concise list of the ranks of indecomposable modules for R a local ring with no condition on the characteristic. We conclude that if the rank of an indecomposable module M is (r,r,…,r), then r∈{1,2,3,4,6}, even when R is not local. 相似文献
12.
Greg Muller 《Journal of Pure and Applied Algebra》2010,214(12):2124-2143
Let D be the ring of differential operators on a smooth irreducible affine variety X over C, or, more generally, the enveloping algebra of any locally free Lie algebroid on X. The category of finitely generated graded modules of the Rees algebra has a natural quotient category PD which imitates the category of modules on Proj of a graded commutative ring. We show that the derived category Db(PD) is equivalent to the derived category of finitely generated modules of a sheaf of algebras E on X which is coherent over X. This generalizes the usual Beilinson equivalence for projective space, and also the Beilinson equivalence for differential operators on a smooth curve used by Ben-Zvi and Nevins in [6] to describe the moduli space of left ideals in D. 相似文献
13.
For digraphs D and H, a mapping f:V(D)→V(H) is a homomorphism ofDtoH if uv∈A(D) implies f(u)f(v)∈A(H). For a fixed directed or undirected graph H and an input graph D, the problem of verifying whether there exists a homomorphism of D to H has been studied in a large number of papers. We study an optimization version of this decision problem. Our optimization problem is motivated by a real-world problem in defence logistics and was introduced recently by the authors and M. Tso.Suppose we are given a pair of digraphs D,H and a cost ci(u) for each u∈V(D) and i∈V(H). The cost of a homomorphism f of D to H is ∑u∈V(D)cf(u)(u). Let H be a fixed digraph. The minimum cost homomorphism problem for H, MinHOMP(H), is stated as follows: For input digraph D and costs ci(u) for each u∈V(D) and i∈V(H), verify whether there is a homomorphism of D to H and, if it does exist, find such a homomorphism of minimum cost. In our previous paper we obtained a dichotomy classification of the time complexity of when H is a semicomplete digraph. In this paper we extend the classification to semicomplete k-partite digraphs, k≥3, and obtain such a classification for bipartite tournaments. 相似文献
14.
. Let d(D) (resp., d(G)) denote the diameter and r(D) (resp., r(G)) the radius of a digraph D (resp., graph G). Let G×H denote the cartesian product of two graphs G and H. An orientation D of G is said to be (r, d)-invariant if r(D)=r(G) and d(D)=d(G). Let {T
i
}, i=1,…,n, where n≥2, be a family of trees. In this paper, we show that the graph ∏
i
=1
n
T
i
admits an (r, d)-invariant orientation provided that d(T
1)≥d(T
2)≥4 for n=2, and d(T
1)≥5 and d(T
2)≥4 for n≥3.
Received: July 30, 1997 Final version received: April 20, 1998 相似文献
15.
Christopher C. Gill 《Archiv der Mathematik》2016,107(2):151-158
Applying an epimorphism of the Solomon descent algebra onto the subring of the Green ring spanned by the isomorphism classes of Young permutation modules, we determine a basis of primitive orthogonal idempotents which diagonalise the multiplication maps of Young permutation modules. We determine direct sum decompositions of tensor products of hook Young permutation modules, the minimal polynomials of all Young permutation modules, and of the Young module Y(r?1,1). 相似文献
16.
Kirby C. Smith 《Linear algebra and its applications》1976,14(1):21-27
Let V be a finite-dimensional vector space over a division ring D, where D is finite-dimensional over its center F. Suppose T is a semi-linear transformation on V with associated automorphism σ of D. The centralizer of T is the ring C(T) of all linear transformations on V which commute with T. If σr is the identity on D for some r ? 1 and no smaller positive power of σ is an inner automorphism, then the center of C(T) is computed to be polynomials in Tr with coefficients from F0, where F0 is the subfield of F left elementwise fixed by σ. A matrix version of this theorem is also given. 相似文献
17.
Alain Escassut 《P-Adic Numbers, Ultrametric Analysis, and Applications》2011,3(4):263-280
Let K be an algebraically closed field complete with respect to a dense ultrametric absolute value |.|. Let D be an infraconnected affinoid subset of K and let H(D) be the Banach algebra of analytic elements on D. Let f ∈ H(D) be injective in D and let f * be the mapping defined on the multiplicative spectrum of H(D) that identifies with the set of circular filters on D. We show that f * is injective and maps bijectively the Shilov boundary of H(D) onto this of H(f(D)). Thanks to this property we give a new proof of the equality $\left| {f(x) - f(y)} \right| = \left| {x - y} \right|\sqrt {\left| {f'(x)f'(y)} \right|} $ . 相似文献
18.
Let G be a reductive group, defined over the Galois field ${\mathbb{F}_p}$ with p being good for G. Using support varieties and covering techniques based on G r T-modules, we determine the position of simple modules and baby Verma modules within the stable Auslander?CReiten quiver ?? s (G r ) of the rth Frobenius kernel of G. In particular, we show that the almost split sequences terminating in these modules usually have an indecomposable middle term. Concerning support varieties, we introduce a reduction technique leading to isomorphisms $$\mathcal{V}_{G_r}(Z_r(\lambda)) \cong \mathcal{V}_{G_{r-d}}(Z_{r-d}(\mu))$$ for baby Verma modules of certain highest weights ${\lambda, \mu \in X(T)}$ , which are related by the notion of depth. 相似文献
19.
For digraphs D and H, a mapping f:V(D)→V(H) is a homomorphism of D to H if uv∈A(D) implies f(u)f(v)∈A(H). For a fixed digraph H, the homomorphism problem is to decide whether an input digraph D admits a homomorphism to H or not, and is denoted as HOM(H).An optimization version of the homomorphism problem was motivated by a real-world problem in defence logistics and was introduced in Gutin, Rafiey, Yeo and Tso (2006) [13]. If each vertex u∈V(D) is associated with costs ci(u),i∈V(H), then the cost of the homomorphism f is ∑u∈V(D)cf(u)(u). For each fixed digraph H, we have the minimum cost homomorphism problem forH and denote it as MinHOM(H). The problem is to decide, for an input graph D with costs ci(u),u∈V(D),i∈V(H), whether there exists a homomorphism of D to H and, if one exists, to find one of minimum cost.Although a complete dichotomy classification of the complexity of MinHOM(H) for a digraph H remains an unsolved problem, complete dichotomy classifications for MinHOM(H) were proved when H is a semicomplete digraph Gutin, Rafiey and Yeo (2006) [10], and a semicomplete multipartite digraph Gutin, Rafiey and Yeo (2008) [12] and [11]. In these studies, it is assumed that the digraph H is loopless. In this paper, we present a full dichotomy classification for semicomplete digraphs with possible loops, which solves a problem in Gutin and Kim (2008) [9]. 相似文献
20.
If v is a norm on n, let H(v) denote the set of all norm-Hermitians in nn. Let S be a subset of the set of real diagonal matrices D. Then there exists a norm v such that S=H(v) (or S = H(v)∩D) if and only if S contains the identity and S is a subspace of D with a basis consisting of rational vectors. As a corollary, it is shown that, for a diagonable matrix h with distinct eigenvalues λ1,…, λr, r?n, there is a norm v such that h ∈ H(v), but hs?H(v), for some integer s, if and only if λ2–λ1,…, λr–λ1 are linearly dependent over the rationals. It is also shown that the set of all norms v, for which H(v) consists of all real multiples of the identity, is an open, dense subset, in a natural metric, of the set of all norms. 相似文献