共查询到20条相似文献,搜索用时 31 毫秒
1.
DRAŽEN ADAMOVIĆ 《Transformation Groups》2016,21(2):299-327
We shall first present an explicit realization of the simple N = 4 superconformal vertex algebra L c N?=?4 with central charge c = ?9. This vertex superalgebra is realized inside of the bcβγ system and contains a subalgebra isomorphic to the simple affine vertex algebra L A1 \( \left(-\frac{3}{2}{\varLambda}_0\right) \). Then we construct a functor from the category of L c N?=?4 -modules with c = ?9 to the category of modules for the admissible affine vertex algebra L A1 \( \left(-\frac{3}{2}{\varLambda}_0\right) \). By using this construction we construct a family of weight and logarithmic modules for L c N?=?4 and L A1 \( \left(-\frac{3}{2}{\varLambda}_0\right) \). We also show that a coset subalgebra L A1 \( \left(-\frac{3}{2}{\varLambda}_0\right) \) is a logarithmic extension of the W(2; 3)-algebra with c = ?10. We discuss some generalizations of our construction based on the extension of affine vertex algebra L A1 (kΛ 0) such that k + 2 = 1/p and p is a positive integer. 相似文献
2.
A. V. Grishin 《Mathematical Notes》2018,104(1-2):22-28
The paper studies the additive structure of the algebra F(7), i.e., a relatively free associative countably generated algebra with the identity [x1,..., x7] = 0 over an infinite field of characteristic ≠ 2, 3. First, the space of proper multilinear polynomials in this algebra is investigated. As an application, estimates for the codimensions cn = dimFn(7) are obtained, where Fn(7) stands for the subspace of multilinear polynomials of degree n in the algebra F(7). 相似文献
3.
A new functor from <Emphasis Type="Italic">D</Emphasis><Subscript>5</Subscript>-Mod to <Emphasis Type="Italic">E</Emphasis><Subscript>6</Subscript>-Mod
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Xiao Ping Xu 《数学学报(英文版)》2016,32(8):867-892
We find a new representation of the simple Lie algebra of type E 6 on the polynomial algebra in 16 variables, which gives a fractional representation of the corresponding Lie group on 16-dimensional space. Using this representation and Shen’s idea of mixed product, we construct a new functor from D 5-Mod to E 6-Mod. A condition for the functor to map a finite-dimensional irreducible D 5-module to an infinite-dimensional irreducible E 6-module is obtained. Our results yield explicit constructions of certain infinite-dimensional irreducible weight E6-modules with finite-dimensional weight subspaces. In our approach, the idea of Kostant’s characteristic identities plays a key role. 相似文献
4.
A k-total coloring of a graph G is a mapping ?: V (G) ? E(G) → {1; 2,..., k} such that no two adjacent or incident elements in V (G) ? E(G) receive the same color. Let f(v) denote the sum of the color on the vertex v and the colors on all edges incident with v: We say that ? is a k-neighbor sum distinguishing total coloring of G if f(u) 6 ≠ f(v) for each edge uv ∈ E(G): Denote χ Σ ″ (G) the smallest value k in such a coloring of G: Pil?niak and Wo?niak conjectured that for any simple graph with maximum degree Δ(G), χ Σ ″ ≤ Δ(G)+3. In this paper, by using the famous Combinatorial Nullstellensatz, we prove that for K 4-minor free graph G with Δ(G) > 5; χ Σ ″ = Δ(G) + 1 if G contains no two adjacent Δ-vertices, otherwise, χ Σ ″ (G) = Δ(G) + 2. 相似文献
5.
Let G be a 2-edge-connected simple graph on n vertices. For an edge e = uv ∈ E(G), define d(e) = d(u) + d(v). Let F denote the set of all simple 2-edge-connected graphs on n ≥ 4 vertices such that G ∈ F if and only if d(e) + d(e’) ≥ 2n for every pair of independent edges e, e’ of G. We prove in this paper that for each G ∈ F, G is not Z 3-connected if and only if G is one of K 2,n?2, K 3,n?3, K 2,n?2 + , K 3,n?3 + or one of the 16 specified graphs, which generalizes the results of X. Zhang et al. [Discrete Math., 2010, 310: 3390–3397] and G. Fan and X. Zhou [Discrete Math., 2008, 308: 6233–6240]. 相似文献
6.
7.
K. V. Storozhuk 《Siberian Mathematical Journal》2010,51(2):330-337
Let T t : X → X be a C 0-semigroup with generator A. We prove that if the abscissa of uniform boundedness of the resolvent s 0(A) is greater than zero then for each nondecreasing function h(s): ?+ → R + there are x′ ∈ X′ and x ∈ X satisfying ∫ 0 ∞ h(|〈x′, T x x〉|)dt = ∞. If i? ∩ Sp(A) ≠ Ø then such x may be taken in D(A ∞). 相似文献
8.
Let F be a non-archimedean local field. We study the restriction of irreducible admissible genuine representations of the twofold metaplectic cover \({\widetilde {GL}_2}\) of GL2(F) to the inverse image in \({\widetilde {GL}_2}\) of a maximal torus in GL2(F). 相似文献
9.
Commutator of Riesz potential in <Emphasis Type="Italic">p</Emphasis>-adic generalized Morrey spaces
Suppose that I p α is the p-adic Riesz potential. In this paper, we established the boundedness of I p α on the p-adic generalized Morrey spaces, as well as the boundedness of the commutators generated by the p-adic Riesz potential I p α and p-adic generalized Campanato functions. 相似文献
10.
We prove the existence of a completely integrable Pfaffian system ?x/?t i = A i (t)x, x ∈ R n , t = (t 1, t 2, t 3) ∈ R + 3 , i = 1, 2, 3, with infinitely differentiable bounded coefficients and with lower characteristic set of positive three-dimensional Lebesgue measure. 相似文献
11.
We present an equivalence theorem, which includes all known characterizations of the class B p , i.e., the weight class of Ariño and Muckenhoupt, and also some new equivalent characterizations. We also give equivalent characterizations for the classes B p * , B ∞ * and RB p , and prove and apply a “gluing lemma” of independent interest. 相似文献
12.
Given an indexing set I and a finite field Kα for each α ∈ I, let ? = {L2(Kα) | α ∈ I} and \(\mathfrak{N} = \{ SL_2 (K_\alpha )|\alpha \in I\}\). We prove that each periodic group G saturated with groups in \(\Re (\mathfrak{N})\) is isomorphic to L2(P) (respectively SL2(P)) for a suitable locally finite field P. 相似文献
13.
Let \({\mathscr {N}}\) be a 2-step nilpotent Lie algebra endowed with a non-degenerate scalar product \(\langle .\,,.\rangle \), and let \({\mathscr {N}}=V\oplus _{\perp }Z\), where Z is the centre of the Lie algebra and V its orthogonal complement. We study classification of the Lie algebras for which the space V arises as a representation space of the Clifford algebra \({{\mathrm{{\mathrm{Cl}}}}}({\mathbb {R}}^{r,s})\), and the representation map \(J:{{\mathrm{{\mathrm{Cl}}}}}({\mathbb {R}}^{r,s})\rightarrow {{\mathrm{End}}}(V)\) is related to the Lie algebra structure by \(\langle J_zv,w\rangle =\langle z,[v,w]\rangle \) for all \(z\in {\mathbb {R}}^{r,s}\) and \(v,w\in V\). The classification depends on parameters r and s and is completed for the Clifford modules V having minimal possible dimension, that are not necessary irreducible. We find necessary conditions for the existence of a Lie algebra isomorphism according to the range of the integer parameters \(0\le r,s<\infty \). We present a constructive proof for the isomorphism maps for isomorphic Lie algebras and determine the class of non-isomorphic Lie algebras. 相似文献
14.
Let g be the finite dimensional simple Lie algebra of type An, and let U? = U q (g,Λ) and U = U q (g,Q) be the quantum groups defined over the weight lattice and over the root lattice, respectively. In this paper, we find two algebraically independent central elements in U? for all n ≥ 2 and give an explicit formula of the Casimir elements for the quantum group U? = U q (g,Λ), which corresponds to the Casimir element of the enveloping algebra U(g). Moreover, for n = 2 we give explicitly generators of the center subalgebras of the quantum groups U? = U q (g,Λ) and U = U q (g,Q). 相似文献
15.
F. Galaz-Fontes 《Positivity》2010,14(4):715-729
For a vector measure ν having values in a real or complex Banach space and \({p \in}\) [1, ∞), we consider L p (ν) and \({L_{w}^{p}(\nu)}\), the corresponding spaces of p-integrable and scalarly p-integrable functions. Given μ, a Rybakov measure for ν, and taking q to be the conjugate exponent of p, we construct a μ-Köthe function space E q (μ) and show it is σ-order continuous when p > 1. In this case, for the associate spaces we prove that L p (ν) × = E q (μ) and \({E_q(\mu)^\times = L_w^p(\nu)}\). It follows that \({L_p (\nu) ^{**} = L_w^p (\nu)}\). We also show that L 1 (ν) × may be equal or not to E ∞ (μ). 相似文献
16.
<Emphasis Type="Italic">V</Emphasis>-Gorenstein injective modules preenvelopes and related dimension
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Let R and S be associative rings and S V R a semidualizing (S-R)-bimodule. An R-module N is said to be V-Gorenstein injective if there exists a Hom R (I V (R),?) and Hom R (?,I V (R)) exact exact complex \( \cdots \to {I_1}\xrightarrow{{{d_0}}}{I_0} \to {I^0}\xrightarrow{{{d_0}}}{I^1} \to \cdots \) of V-injective modules I i and I i , i ∈ N0, such that N ? Im(I 0 → I 0). We will call N to be strongly V-Gorenstein injective in case that all modules and homomorphisms in the above exact complex are equal, respectively. It is proved that the class of V-Gorenstein injective modules are closed under extension, direct summand and is a subset of the Auslander class A V (R) which leads to the fact that V-Gorenstein injective modules admit exact right I V (R)-resolution. By using these facts, and thinking of the fact that the class of strongly V-Gorenstein injective modules is not closed under direct summand, it is proved that an R-module N is strongly V-Gorenstein injective if and only if N ⊕ E is strongly V-Gorenstein injective for some V-injective module E. Finally, it is proved that an R-module N of finite V-Gorenstein injective injective dimension admits V-Gorenstein injective preenvelope which leads to the fact that, for a natural integer n, Gorenstein V-injective injective dimension of N is bounded to n if and only if \(Ext_{{I_V}\left( R \right)}^{ \geqslant n + 1}\left( {I,N} \right) = 0\) for all modules I with finite I V (R)-injective dimension. 相似文献
17.
A. A. Kirillov 《Functional Analysis and Its Applications》2008,42(4):308-316
We give an explicit formula for the exterior powers ∧ k π 1 of the defining representation π 1 of the simple Lie algebra ?ο(2n + 1, ?). We use the technique of family algebras. All representations in question are children of the spinor representation σ of g2ο(2n + 1, ?). We also give a survey of main results on family algebras. 相似文献
18.
In our previous papers, we introduced the notion of a generalized solution to the initial-boundary value problem for the wave equation with a boundary function µ(t) such that the integral ∫ 0 T (T ? t)|µ(t)| p dt exists. Here we prove that this solution is a unique solution to the problem in L p that satisfies the corresponding integral identity. 相似文献
19.
V. I. Zenkov 《Siberian Mathematical Journal》2018,59(2):264-269
Given a finite group G with socle isomorphic to L n (2 m ), we describe (up to conjugacy) all ordered pairs of primary subgroups A and B in G such that A ∩ B g ≠ 1 for all g ∈ g. 相似文献
20.
Let R be a subring ring of Q. We reserve the symbol p for the least prime which is not a unit in R; if R ?Q, then p=∞. Denote by DGL n np , n≥1, the category of (n-1)-connected np-dimensional differential graded free Lie algebras over R. In [1] D. Anick has shown that there is a reasonable concept of homotopy in the category DGL n np . In this work we intend to answer the following two questions: Given an object (L(V), ?) in DGL n 3n+2 and denote by S(L(V), ?) the class of objects homotopy equivalent to (L(V), ?). How we can characterize a free dgl to belong to S(L(V), ?)? Fix an object (L(V), ?) in DGL n 3n+2 . How many homotopy equivalence classes of objects (L(W), δ) in DGL n 3n+2 such that H * (W, d′)?H * (V, d) are there? Note that DGL n 3n+2 is a subcategory of DGL n np when p>3. Our tool to address this problem is the exact sequence of Whitehead associated with a free dgl. 相似文献