Generalizations of pseudo MV-algebras and generalized pseudo effect algebras

We deal with unbounded dually residuated lattices that generalize pseudo MV-algebras in such a way that every principal order-ideal is a pseudo MV-algebra. We describe the connections of these generalized pseudo MV-algebras to generalized pseudo effect algebras, which allows us to represent every generalized pseudo MV-algebra A by means of the positive cone of a suitable ℓ-group G _A . We prove that the lattice of all (normal) ideals of A and the lattice of all (normal) convex ℓ-subgroups of G _A are isomorphic. We also introduce the concept of Archimedeanness and show that every Archimedean generalized pseudo MV-algebra is commutative. Supported by the Research and Development Council of the Czech Govenrment via the project MSM6198959214.     

Schreier rewriting beyond the classical setting Dedicated to our teacher Alfred Lvovich Shmelkin on his 70th birthday

Using actions of free monoids and free associative algebras, we establish some Schreier-type formulas involving ranks of actions and ranks of subactions in free actions or Grassmann-type relations for the ranks of intersections of subactions of free actions. The coset action of the free group is used to establish a generalization of the Schreier formula in the case of subgroups of infinite index. We also study and apply large modules over free associative and free group algebras.     

Construct irreducible representations of quantum groups U q (ƒ m (K))

In this paper, we construct families of irreducible representations for a class of quantum groups U _q (ƒ _m (K)). First, we give a natural construction of irreducible weight representations for U _q (ƒ _m (K)) using methods in spectral theory developed by Rosenberg. Second, we study the Whittaker model for the center of U _q (ƒ _m (K)). As a result, the structure of Whittaker representations is determined, and all irreducible Whittaker representations are explicitly constructed. Finally, we prove that the annihilator of a Whittaker representation is centrally generated.      

一个新的高维向量Lie代数及其应用

构造了一个新的8维向量Lie代数,通过适当设计等谱问题,利用屠格式和扩展的迹恒等式得到了AKNS族的可积耦合及Hamilton结构.     

Einstein solvmanifolds with a simple Einstein derivation

The structure of a solvable Lie group admitting an Einstein left-invariant metric is, in a sense, completely determined by the nilradical of its Lie algebra. We give an easy-to-check necessary and sufficient condition for a nilpotent algebra to be an Einstein nilradical whose Einstein derivation has simple eigenvalues. As an application, we classify filiform Einstein nilradicals (modulo known classification results on filiform graded Lie algebras).      

Cosemisimple Coextensions and Homological Dimension of Smash Coproducts

Let H be a finite dimensional cosemisimple Hopf algebra, C a left H-comodule coalgebra and let C = C/C（H^＊）^＋ be the quotient coalgebra and the smash coproduct of C and H. It is shown that if C/C is a eosemisimple coextension and C is an injective right C-comodule, then gl. dim（the smash coproduct of C and H） = gl. dim（C） = gl. dim（C）, where gl. dim（C） denotes the global dimension of coalgebra C.     

Irreversible helix rearrangement from Cis‐transoid to Cis‐cisoid in poly(p‐n‐hexyloxyphenylacetylene) induced by heat‐treatment in solid phase

Polymerization of p‐n‐hexyloxyphenylacetylene (pHPA) by using a [Rh(norbornadine)Cl]₂‐triethylamine catalyst was carried out at room temperature to afford stereoregular helical poly(p‐n‐hexyloxyphenylacetylene)s (PpHPAs). When ethanol and n‐hexane were used as polymerization solvents, a bright yellow PpHPAs, poly( Y ) with M_n = 8.5 × 10⁴ and its purple red polymer, poly( R ) with M_n = 5.3 × 10⁴ were obtained in 95% yields and 84% yields, respectively. Diffuse reflective UV–vis spectra of poly( Y ) and poly( R ) in solid phase showed different broad absorption peaks at 445 and 575 nm, respectively. X‐Ray diffraction patterns of poly( Y ) and poly( R ) showed typical columnar structures assignable to cis‐transoid and cis‐cisoid structures, respectively, which were also supported by molecule mechanics calculation. Poly( Y ) was irreversibly transformed to a reddish‐black polymer, poly( Y‐B ), which columnar diameter was nearly the same as that of poly( R ). Further, poly( Y ) showed an exothermic peak in the differential scanning calorimetry trace at 80 °C for 1 h in N₂ gas. Thus, these findings suggest a thermally irreversible rearrangement from an unstable cis‐transoid form, poly( Y ) with a stretched cis‐transoid helix to a stable cis‐cisoid form, poly( R ), with a contracted cis‐cisoid helix in the solid phase to give poly( Y → B ) with the cis‐cisoid form. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

A New Expression of the Fractional Fourier Transformation

With the help of su(2) algebra technique, a new equivalent form of the fractional Fourier transformation is given. Two examples are illustrated for their physical application in quantum optics.``