Jucys-Murphy elements and centers of cellular algebras

Let R be an integral domain and A a cellular algebra. Suppose that A is equipped with a family of Jucys-Murphy elements which satisfy the separation condition. Let K be the field of fractions of R. We give a necessary and sufficient condition under which the center of $A_{K}$ consists of the symmetric polynomials in Jucys-Murphy elements.Comment: 11 page

Nakayama twisted centers and dual bases of Frobenius cellular algebras

For a Frobenius cellular algebra, we prove that if the left (right) dual basis of a cellular basis is again cellular, then the algebra is symmetric. Moreover, some ideals of the center are constructed by using the so-called Nakayama twisted center.Comment: 12 page

Centers of symmetric cellular algebras

Let $R$ be an integral domain and $A$ a symmetric cellular algebra over $R$ with a cellular basis \{C_{S,T}^\lam \mid \lam\in\Lambda, S,T\in M(\lam)\}. We will construct an ideal $L(A)$ of the center of $A$ and prove that $L(A)$ contains the so-called Higman ideal. When $R$ is a field, we prove that the dimension of $L(A)$ is not less than the number of non-isomorphic simple $A$-modules.Comment: 14 page

Radicals of symmetric cellular algebras

Let A be a finite dimensional symmetric cllular algebras. We construct a nilpotent ideal in A. The ideal connects the radicals of cell modules with the radical of the algebra. It also reveals some information on the dimensions of simple modules of A.Comment: 15 page

On a global supersonic-sonic patch characterized by 2-D steady full Euler equations

Supersonic-sonic patches are ubiquitous in regions of transonic flows and they boil down to a family of degenerate hyperbolic problems in regions surrounded by a streamline, a characteristic curve and a possible sonic curve. This paper establishes the global existence of solutions in a whole supersonic-sonic patch characterized by the two-dimensional full system of steady Euler equations and studies solution behaviors near sonic curves, depending on the proper choice of boundary data extracted from the airfoil problem and related contexts. New characteristic decompositions are developed for the full system and a delicate local partial hodograph transformation is introduced for the solution estimates. It is shown that the solution is uniformly $C^{1,\frac{1}{6}}$ continuous up to the sonic curve and the sonic curve is also $C^{1,\frac{1}{6}}$ continuous.Comment: 34 page

Fusion procedure for Degenerate cyclotomic Hecke algebras

The primitive idempotents of the generic degenerate cycloctomic Hecke algebras are derived by consecutive evaluations of a certain rational function. This rational function depends only on the Specht modules and the normalization factors are the weights of the Brundan-Kleshchev trace.Comment: 10 page

Jordan Derivations and Lie derivations on Path Algebras

Without the faithful assumption, we prove that every Jordan derivation on a class of path algebras of quivers without oriented cycles is a derivation and that every Lie derivation on such kinds of algebras is of the standard form.Comment: 12 page

Lie Derivations of Dual Extension Algebras

Let $K$ be a field and $\Gamma$ a finite quiver without oriented cycles. Let $\Lambda$ be the path algebra $K(\Gamma, \rho)$ and let $\mathscr{D}(\Lambda)$ be the dual extension of $\Lambda$. In this paper, we prove that each Lie derivation of $\mathscr{D}(\Lambda)$ is of the standard form.Comment: 16 page

Jordan Derivations of some extension algebras

In this paper, we mainly study Jordan derivations of dual extension algebras and those of generalized one-point extension algebras. It is shown that every Jordan derivation of dual extension algebras is a derivation. As applications, we obtain that every Jordan generalized derivation and every generalized Jordan derivation on dual extension algebras are both generalized derivations. For generalized one-point extension algebras, it is proved that under certain conditions, each Jordan derivation of them is the sum of a derivation and an anti-derivation.Comment: 14 page

Adaptive generalized multiscale finite element methods for H(curl)-elliptic problems with heterogeneous coefficients

In this paper, we construct an adaptive multiscale method for solving H(curl)-elliptic problems in highly heterogeneous media. Our method is based on the generalized multiscale finite element method. We will first construct a suitable snapshot space, and a dimensional reduction procedure to identify important modes of the solution. We next develop and analyze an a posteriori error indicator, and the corresponding adaptive algorithm. In addition, we will construct a coupled offline-online adaptive algorithm, which provides an adaptive strategy to the selection of offline and online basis functions. Our theory shows that the convergence is robust with respect to the heterogeneities and contrast of the media. We present several numerical results to illustrate the performance of our method