Characteristic modules and tensor products over quasi-hereditary algebras

Let A be a monomial quasi-hereditary algebra with a pure strong exact Borel subalgebra B.It is proved that the category of induced good modules over B is contained in the category of good modules over A;that the characteristic module of A is an induced module of that of B via the exact functor-(?)_B A if and only if the induced A-module of an injective B-module remains injective as a B-module.Moreover,it is shown that an exact Borel subalgebra of a basic quasi-hereditary serial algebra is right serial and that the characteristic module of a basic quasi-hereditary serial algebra is exactly the induced module of that of its exact Borel subalgebra.     

限制李超代数的诱导模

In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established. Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules.     

On the Algebraic Functional Equation of the Eigenspaces of Mixed Signed Selmer Groups of Elliptic Curves with Good Reduction at Primes above p

Let p be an odd prime number,and let E be an elliptic curve defined over a number field which has good reduction at every prime above p.Under suitable assumptions,we prove that the η-eigenspace and the ■-eigenspace of mixed signed Selmer group of the elliptic curve are pseudoisomorphic.As a corollary,we show that the η-eigenspace is trivial if and only if the ■-eigenspace is trivial.Our results can be thought as a reflection principle which relates an Iwasawa module in a given eigenspace with another Iwasawa module in a "reflected" eigenspace.     

An Example Using Improved Lefschetz Duality

A theorem of Lambrechts and Stanley is used to find the rational cohomology of the complement of an embedding S~(4n-1)→ S~(2n)× S~m as a module and demonstrate that it is not necessarily determined by the map induced on cohomology by the embedding, nor is it a trivial extension. This demonstrates that the theorem is an improvement on the classical Lefschetz duality.     

Number of Induced Matchings of Graphs

A matching M of a graph G is an induced matching if no two edges in M arejoined by an edge of G.Let iz(G) denote the total number of induced matchings of G,named iz-index.It is well known that the Hosoya index of a graph is the total number of matchings and the Hosoya index of a path can be calculated by the Fibonacci sequence.In this paper,we investigate the iz-index of graphs by using the Fibonacci-Narayana sequence and characterize some types of graphs with minimum and maximum iz-index,respec...     

Classification of Irreducible Weight Modules with a Finite-dimensional Weight Space over Twisted Heisenberg-Virasoro Algebra

We show that the support of an irreducible weight module over the twisted Heisenberg-Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite dimensional. As a corollary, we obtain that every irreducible weight module over the twisted Heisenber-Virasoro algebra, having a nontrivial finite-dimensional weight space, is a Harish-Chandra module （and hence is either an irreducible highest or lowest weight module or an irreducible module from the intermediate series）.     

Frobenius morphisms and stable module categories of repetitive algebras

Let k be the algebraic closure of a finite field F_q and A be a finite dimensional k-algebra with a Frobenius morphism F.In the present paper we establish a relation between the stable module category of the repetitive algebra  of A and that of the repetitive algebra of the fixed-point algebra A~F.As an application,it is shown that the derived category of A~F is equivalent to the subcategory of F-stable objects in the derived category of A when A has a finite global dimension.     

Irreducible weight modules over the twisted Schrödinger-Virasoro algebra

It is shown that the support of an irreducible weight module over the SchrSdinger-Virasoro Lie algebra with an infinite-dimensional weight space coincides with the weight lattice, and all nontrivial weight spaces of such a module are infinite-dimensional. As a by-product, it is obtained that every simple weight module over Lie algebra of this type with a nontrivial finite-dimensional weight space is a Harish-Chandra module.     

Über den grössten p-Normalteiler einer endlichen Gruppe

If G is a finite group and A a Hall p'-subgroup of G, then it is well known that O_p(G) is the largest p-subgroup of G, which is normalized by A. In this note, O_p(G) is characterized as the largest p-subgroup, whose normalizer contains a Sylow p-subgroup of G and the generalized Fittingsubgroup of A.     

Affine Module Groups and Their Automorphisms

An affine module group is a semidirect extension of an additive module group by its automorphism group. Maximal Abelian normal subgroups of an affine group are described. It is proved that operator isomorphisms of affine groups are induced by module automorphisms. Automorphisms of an affine group which do not leave a module fixed are treated. And conditions are specified for a module to be non-characteristic in its affine group.     

拟遗传代数的诱导模与广义Betti数

本文引入了模的广义Betti数,给出了经典Betti数与广义Betti数之间的关系,证明了具有纯粹强正合Borel子代数的零关系拟遗传代数的诱导模的极小投射分解可通过其正合Borel子代数的相应模的极小投射分解的诱导给出,从而两者具有相同的广义Betti数.     

Differential projective modules over differential rings

Differential modules over a commutative differential ring which are projective as ring modules, with differential homomorphisms, form an additive category. Every projective ring module is shown occurs as the underlying module of a differential module. Differential modules, projective as ring modules, are shown to be direct summands of differential modules free as ring modules; those which are differential direct summands of differential direct sums of the ring being induced from the subring of constants. Every differential module finitely generated and projective as a ring module is shown to have this form after a faithfully flat finitely presented differential extension of the base.     

Peristatcally induced MHD slip flow in a porous medium due to a surface acoustic wavy wall

The influences of Hall current and slip condition on the MHD flow induced by sinusoidal peristaltic wavy wall in two dimensional viscous fluid through a porous medium for moderately large Reynolds number is considered on the basis of boundary layer theory in the case where the thickness of the boundary layer is larger than the amplitude of the wavy wall. Solutions are obtained in terms of a series expansion with respect to small amplitude by a regular perturbation method. Graphs of velocity components, both for the outer and inner flows for various values of the Reynolds number, slip parameter, Hall and magnetic parameters are drawn. The inner and outer solutions are matched by the matching process. An interesting application of the present results to mechanical engineering may be the possibility of the fluid transportation without an external pressure.     

Nonzero level Harish-Chandra modules over the Virasoro-like algebra

In the present paper, we study the nonzero level Harish-Chandra modules for the Virasoro-like algebra. We prove that a nonzero level Harish-Chandra module of the Virasoro-like algebra is a generalized highest weight (GHW for short) module. Then we prove that a GHW module of the Virasoro-like algebra is induced from an irreducible module of a Heisenberg subalgebra.     

Effect of Hall currents on interaction of pulsatile and peristaltic transport induced flows of a particle-fluid suspension

The interaction of purely periodic mean flow with a peristaltic induced flow is investigated within the framework of a two-dimensional analogue. The mathematical model considers a viscous incompressible fluid under the effect of transverse magnetic field, taking into account the effect of Hall currents for a magneto-fluid with suspended particles between infinite parallel walls on which a sinusoidal traveling wave is imposed. A perturbation solution to the complete set of Navier-Stokes equations is found for the case in which the frequency of the traveling wave and that of the imposed pressure gradient are equal. The ratio of the traveling wave amplitude to channel width is assumed to be small. For this case a first order steady flow is found to exist, as contrasted to a second order effect in the absence of the imposed periodic pressure gradient. The effect of Hall parameter, Hartmann number and the various parameters included in the problem are discussed numerically.     

Irreducible modules and normal subgroups of prime index

Let F be a field, G a finite group, H a normal subgroup of prime index p, and V an irreducible FH-module. If F is algebraically closed and of characteristic 0, the FG-module induced from V is either irreducible or a direct sum of p pairwise nonisomorphic irreducible modules. It is shown here that if F is not assumed algebraically closed and its characteristic is not 0, then there are not two but six possibilities for the structure of the induced module.