Isomorphically rigid algebras

Various classes of non-associative algebras possessing the property of being rigid under abstract isomorphisms are studied. Supported by RFBR grant No. 06-01-00159a. __________ Translated from Algebra i Logika, Vol. 46, No. 4, pp. 483–502, July–August, 2007.     

Corner view on the crown domain

In this paper we raise a question about the boundary of the crown domain of a Riemannian symmetric space X. In case X is of Hermitian type we give an affirmative answer.     

A reply to “a comment on generalized electromagnetism and Dirac algebra”

Issues raised by W. A. Rodrigues, Jr. are discussed.1. This is not a new result; see,e.g., Rohrlich.⁽³⁾ 2. A typographical error in Eq. (77) is corrected here: The productj A in the right-hand parentheses was erroneously transcribed in Ref. (2) as A.3. I define electromagnetic fieldF = A to be that generated by electric charges and the magnetoelectric fieldG = M to be that generated by magnetic monopoles:F F +₅ G. 4. Rodrigues, on the other hand, takes the position that the importance of the Lagrangian formulation should be downgraded if not discarded altogether: ... it is redundant to look for Lagrangians.⁽¹⁾ 5. In fact, he reformulates it using the language of differential forms.6. It is interesting to observe that this bilinear form has the additional virtue of being appropriate for dealing with the monopolecharge parity question, which was pointed out long ago.⁽¹⁴⁾ 7. In fact, even mathematics looks to Nature for its authority.⁽¹⁶⁾ There is evidence that Rodrigues does not understand this concept.⁽¹⁷⁾     

Automorphisms on a Lie group contracting modulo a compact subgroup and applications to semistable convolution semigroups

Let ( _t ) _t0 be a -semistable convolution semigroup of probability measures on a Lie groupG whose idempotent ₀ is the Haar measure on some compact subgroupK. Then all the measures ₁ are supported by theK-contraction groupC _K() of the topological automorphism ofG. We prove here the structure theoremC _K()=C()K, whereC() is the contraction group of . Then it turns out that it is sufficient to study semistable convolution semigroups on simply connected nilpotent Lie groups that have Lie algebras with a positive graduation.     

一阶导数吸光光度法测定碘酸钾碘盐中碘

采用一阶导数吸光光度法测定碘酸钾碘盐中碘 ,线性范围为 0～ 12 μg·ml-1,检出限为1.6μg·ml-1,对盐样进行重复测定 ,相对标准偏差≤ 1.9% ,对样品进行加标回收试验 ,回收率在 97.0 %～ 10 2 .5 % ,结果良好     

On deformed preprojective algebras

Deformed preprojective algebras are generalizations of the usual preprojective algebras introduced by Crawley-Boevey and Holland, which have applications to Kleinian singularities, the Deligne-Simpson problem, integrable systems and noncommutative geometry. In this paper we offer three contributions to the study of such algebras: (1) the 2-Calabi-Yau property; (2) the unification of the reflection functors of Crawley-Boevey and Holland with reflection functors for the usual preprojective algebras; and (3) the classification of tilting ideals in 2-Calabi-Yau algebras, and especially in deformed preprojective algebras for extended Dynkin quivers.     

Axiomatizing subcategories of Abelian categories

We investigate how to characterize subcategories of abelian categories in terms of intrinsic axioms. In particular, we find axioms which characterize generating cogenerating functorially finite subcategories, precluster tilting subcategories, and cluster tilting subcategories of abelian categories. As a consequence we prove that any d-abelian category is equivalent to a d-cluster tilting subcategory of an abelian category, without any assumption on the categories being projectively generated.     

Canonical Connections and Algebraic Ricci Solitons of Three-dimensional Lorentzian Lie Groups

In this paper, the author computes canonical connections and KobayashiNomizu connections and their curvature on three-dimensional Lorentzian Lie groups with some product structure. He defines algebraic Ricci solitons associated to canonical connections and Kobayashi-Nomizu connections. He classifies algebraic Ricci solitons associated to canonical connections and Kobayashi-Nomizu connections on three-dimensional Lorentzian Lie groups with some product structure.     

一类自伴随Lubrication方程的对称,守恒律,拉格朗日函数和精确解

本文借助李对称分析研究了一类自伴随的Lubrication方程,此类方程可用来描述液体薄膜动力学行为.基于非奇异的局域守恒律乘子和李对称方法,我们系统地推导出了此类方程的局域守恒律,非局域相关系统,李对称和一些有趣的精确解.此模型的非局域相关系统在本文中被首次研究,可用于寻找原方程更丰富的解空间.此外,基于局域守恒律和变分原则,我们推导出原方程的四类拉格朗日函数.     

Left invariant special Kähler structures

We construct left invariant special Kähler structures on the cotangent bundle of a flat pseudo-Riemannian Lie group. We introduce the twisted cartesian product of two special Kähler Lie algebras according to two linear representations by infinitesimal Kähler transformations. We also exhibit a double extension process of a special Kähler Lie algebra which allows us to get all simply connected special Kähler Lie groups with bi-invariant symplectic connections. All Lie groups constructed by performing this double extension process can be identified with a subgroup of symplectic (or Kähler) affine transformations of its Lie algebra containing a nontrivial 1-parameter subgroup formed by central translations. We show a characterization of left invariant flat special Kähler structures using étale Kähler affine representations, exhibit some immediate consequences of the constructions mentioned above, and give several non-trivial examples.