Combinatorially Factorizable Inverse Monoids

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Coset Decomposition for Semisimple Hopf Algebras

The notion of double coset for semisimple finite dimensional Hopf algebras is introduced. This is done by considering an equivalence relation on the set of irreducible characters of the dual Hopf algebra. As an application formulae for the restriction of the irreducible characters to normal Hopf subalgebras are given.     

Equivaleces between D-categories of Inverse Monoids

There exist two equivalent small categories associated to an inverse monoid which reflect its divisorial structure, called its D-categories. It is well known the relationship between the Green's relation D and the structure, of certain subsemigroups, of an inverse monoid. In this work, an analogous result is established between the Green's relation J and the D-categories of those subsemigroups. They are also given equivalent conditions for the equivalence of the D-categories of two inverse monoids and likewise equivalent conditions for the isomorphism of two inverse monoids in terms of its D-categories. It is proved that for many important classes of inverse monoids the multiplicative structure is determined by the associated category. On the contrary, a sufficient condition to obtain families of counterexamples to the above is provided and three examples are explicitely exhibited.     

Multilinear Equations in Free Inverse Monoids

We prove that finding solutions to the class of single multilinear equations in FIM(A) is decidable; while finding solutions to the class of systems of multilinear equations in FIM(A) is undecidable.     

Representations of Inverse Monoids by Partial Automorphisms

It is shown that any inverse semigroup of endomorphisms of an object in a properly (E, M)-structured category admitting intersections may be embedded in an inverse monoid of partial automorphisms between retracts of that object. It follows that every inverse monoid is isomorphic with an inverse monoid of all partial automorphisms between [non-trival] retracts of some object of any [almost] algebraically universal and properly (E, M)-structured category with intersections; in particular, of an [almost] algebraically universal and finitely complete category with arbitrary intersections. Several examples are given.     

On Incidence Algebras of Combinatorial Inverse Monoids

We study the incidence algebra of the reduced standard division category of a combinatorial bisimple inverse monoid [with (E(S), ≤) locally finite], and we describe semigroups of poset type (i.e., a combinatorial inverse semigroup for which the corresponding Möbius category is a poset) as being combinatorial strict inverse semigroups. Up to isomorphism, the only Möbius-division categories are the reduced standard division categories of combinatorial inverse monoids.     

含幺逆半群的半格的同余对

本文利用一族含幺逆半群的同余对刻画了其半格的同余对,并给出了含幺逆半群半格的正规同余对族的格与其标准同余对的格之间的同构关系.     

含幺逆半群的半格上的同余格

本文证明了含幺逆半群Sα（α∈Y）的半格的容许同余格同构于半格S上同余格的一个子格。     

右（左）逆半群的半直积及圈积

给出了两个幺半群的半直积及圈积为右（左）逆半群的充分必要条件，从而推广了[2]中两个幺半群的半幺直积和圈积为逆半群的充分必要条件．     

On a Class of Factorizable Inverse Monoids Associated with Braid Groups

We prove that a constructible nilpotent-by-abelian group G can be obtained from a polycyclic group by forming d successive properly ascending HNN-extensions if and only if d is the dimension of the linear subspace of Hom(G, R) spanned by the geometric invariant Σ¹ (G, Z) ^c . We also obtain a result on the finiteness properties “type FP _m ” of certain subgroups of G     

The Polycyclic Monoids P n and the Thompson Groups V n,1

We construct what we call the strong orthogonal completion C _n of the polycyclic monoid P _n on n generators. The inverse monoid C _n is congruence free and its group of units is the Thompson group V _n,1. Copies of C _n can be constructed from partitions of sets into n blocks each block having the same cardinality as the underlying set.     

集值逆下鞅的Doob分解

假定(X,‖·‖)为实Banach空间,X*为其对偶空间,X*可分.本文证明了实值逆(下)鞅Doob分解定理,在此基础上,利用支撑函数给出了集值逆下鞅可Doob分解的一个充分条件.     

Coset Space Construction for the Conformal Group: Spontaneously Broken Phase and Inverse Higgs Phenomenon

Theoretical and Mathematical Physics - We establish a mathematically rigorous way to construct effective theories resulting from the spontaneous breaking of conformal invariance. We show that the...     

Correction of Two Errors in ‘Topological Properties of Inverse Limits of Free Abelian Monoids’

No abstract. December 8, 1999     

长方形Toeplliz-块矩阵的快速逆Cholesky分解

该文对m×n阶长方形Toeplitz-块矩阵A，提出了一种ATA进行逆Cholesky分解的快速算法．该算法乘法运算次数只有O（mn）次．     

四元数自共轭矩阵的几个定理

In this paper we disscus semi - positive definite self-conjugate matrices on quaternion. The following theorem is proved;Suppose A, B are both semi-positive difinite self-conjugate matrices of order n on quaternion. Then( 1 ) there exists P∈GL_n(Q), such that(?).(2) AB and BA are both the centralizable matrices and they are similar to same a real diagonal matrix.