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1.
该文依据弱Hopf代数的定义给出弱Hopf超代数的定义. 进而利用弱反极取代Hopf代数中反极的方法, 构造一类不是Hopf超代数的弱Hopf超代数wsldq(m|n), 并给出了wsldq(m|n)的PBW基.  相似文献   

2.
By the R-matrix of orthosymplectic quantum superalgebra U q (osp(2l+1|2n)) in the vector representation, we establish the corresponding quantum Hopf superalgebra OSP q (2l + 1|2n). Furthermore, it is shown that OSP q (2l + 1|2n) is coquasitriangular.  相似文献   

3.
Ioana Boca 《代数通讯》2013,41(4):1533-1554
We prove that certain algebra quotients of Hopf algebras are twisted Hopf algebras. On the other handuq (sl(2)) is a crossed product of a central subalgebra with a quotient [Ubar], when q is a root of 1. Using the cocycle involved in this crossed product we construct non-trivial complex cocycles τ and we find the isomorphism classes of the corresponding twisted Hopf algebras τ [Ubar]. These provide complex projective representations of [Ubar] which are not ordinary representations.  相似文献   

4.
This note first describes the basic properties of the skew derivations on the polynomial ringk[X]. As a consequence of these properties it is proved that theq-analogue of the enveloping algebra of sl(2),U q(sl(2)), has a unique action on C[X], where “action” means that C[X] is a module algebra in the Hopf algebra sense. This depends on the fact that the generators of a subalgebra ofU q(sl(2)) described by Woronowicz must act via an automorphism, and the skew derivations associated to it. Both authors were supported by the NSF, S. Montgomery by grant DMS 87-00641, and S. P. Smith by DMS 87-02447.  相似文献   

5.
Explicit upper and lower estimates are given for the norms of the operators of embedding of , n ∈ ?, in L q (dµ), 0 < q < ∞. Conditions on the measure µ are obtained under which the ratio of the above estimates tends to 1 as n → ∞, and asymptotic formulas are presented for these norms in regular cases. As a corollary, an asymptotic formula (as n → ∞) is established for the minimum eigenvalues λ1, n, β , β > 0, of the boundary value problems (?d 2/dx 2) n u(x) = λ|x| β?1, x ∈ (?1, 1), u (k)(±1) = 0, k ∈ {0, 1, ..., n ? 1}.  相似文献   

6.
The main aim of the paper is to study infinite-dimensional representations of the real form U q (u n, 1) of the quantized universal enveloping algebra U q (gl n + 1). We investigate the principal series of representations of U q (u n, 1) and calculate the intertwining operators for pairs of these representations. Some of the principal series representations are reducible. The structure of these representations is determined. Then we classify irreducible representations of U q (u n, 1) obtained from irreducible and reducible principal series representations. All *-representations in this set of irreducible representations are separated. Unlike the classical case, the algebra U q (u n, 1) has finite-dimensional irreducible *-representations.  相似文献   

7.
Representations of quantum superalgebras provide a natural framework in which to model supersymmetric quantum systems. Each quantum superalgebra, belonging to the class of quasi-triangular Hopf superalgebras, contains a universal R-matrix which automatically satisfies the Yang–Baxter equation. Applying the vector representation π, which acts on the vector module V, to the left-hand side of a universal R-matrix gives a Lax operator. In this article a Lax operator is constructed for the quantised orthosymplectic superalgebras U q [osp(m|n)] for all m > 2, n ≥ 0 where n is even. This can then be used to find a solution to the Yang–Baxter equation acting on VVW, where W is an arbitrary U q [osp(m|n)] module. The case W = V is studied as an example. Presented by A. Verschoren.  相似文献   

8.
9.
If the gradient of u(x) is nth power locally integrable on Euclidean n-space, then the integral average over a ball B of the exponential of a constant multiple of |u(x)−uB|n/(n−1), uB=average of u over B, tends to 1 as the radius of B shrinks to zero—for quasi almost all center points. This refines a result of N. Trudinger (1967). We prove here a similar result for the class of gradients in Ln(log(e+L))α, 0?α?n−1. The results depend on a capacitary strong-type inequality for these spaces.  相似文献   

10.
An L(p,q)-labeling of a graph G is an assignment f from vertices of G to the set of non-negative integers {0,1,…,λ} such that |f(u)−f(v)|≥p if u and v are adjacent, and |f(u)−f(v)|≥q if u and v are at distance 2 apart. The minimum value of λ for which G has L(p,q)-labeling is denoted by λp,q(G). The L(p,q)-labeling problem is related to the channel assignment problem for wireless networks.In this paper, we present a polynomial time algorithm for computing L(p,q)-labeling of a bipartite permutation graph G such that the largest label is at most (2p−1)+q(bc(G)−2), where bc(G) is the biclique number of G. Since λp,q(G)≥p+q(bc(G)−2) for any bipartite graph G, the upper bound is at most p−1 far from optimal.  相似文献   

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