892 research outputs found
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 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 be an integral domain and a symmetric cellular algebra over
with a cellular basis \{C_{S,T}^\lam \mid \lam\in\Lambda, S,T\in M(\lam)\}.
We will construct an ideal of the center of and prove that
contains the so-called Higman ideal. When is a field, we prove that the
dimension of is not less than the number of non-isomorphic simple
-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 continuous up to the sonic curve and the sonic
curve is also 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 be a field and a finite quiver without oriented cycles. Let
be the path algebra and let
be the dual extension of . In this paper, we prove that each Lie
derivation of 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
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