Browsing by Author "Penkov, Ivan"

Now showing 1 - 4 of 4
  • Thumbnail Image
    Item
    Bounded Weight Modules for Basic Classical Lie Superalgebras at Infinity
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2022) Grantcharov, Dimitar; Penkov, Ivan; Serganova, Vera
    We classify simple bounded weight modules over the complex simple Lie superalgebras sl(∞|∞) and osp(m|2n), when at least one of m and n equals ∞. For osp(m|2n) such modules are of spinor-oscillator type, i.e., they combine into one the known classes of spinor o(m)-modules and oscillator-type sp(2n)-modules. In addition, we characterize the category of bounded weight modules over osp(m|2n) (under the assumption dimosp(m|2n)=∞) by reducing its study to already known categories of representations of sp(2n), where n possibly equals ∞. When classifying simple bounded weight sl(∞|∞)-modules, we prove that every such module is integrable over one of the two infinite-dimensional ideals of the Lie algebra sl(∞|∞)0¯. We finish the paper by establishing some first facts about the category of bounded weight sl(∞|∞)-modules.
  • Thumbnail Image
    Item
    Diopside marble-like sintered glass-ceramics
    (Offenbach : Verlag der Deutschen Glastechnischen Gesellschaft, 1994) Karamanov, Alexander; Gutsow, Ivan; Penkov, Ivan; Andreev, Julian; Bogdanov, Bogdan
    Experimental results on the synthesis of a new marble-like glass-ceramic material to be used for wall covering are given. The material is prepared by sintering and surface-induced crystallizadon of a precursor frit. In contrast to usual glass-ceramic materials similar to natural marbles and granites, where the major crystalline phase is β-wollastonite (CaO * Si0₂ ) , in the new material diopside (CaO * MgO * 2Si0₂ ) is formed. Due to the enhanced crystallization ability of the initial glasses, the duration of the heat treatment needed for the synthesis of the new materials can be considerably reduced.
  • Thumbnail Image
    Item
    Influence of MoO₃ and ZrO₂ on the crystallization of fluor-mica fusion-cast ceramics
    (Offenbach : Verlag der Deutschen Glastechnischen Gesellschaft, 1999) Penkov, Ivan
    Nucleation and crystallization behavior of fluor-mica fusion-cast ceramics has been investigated. By contrast to oxide glasses, fusioncast ceramics based on potassium or barium fluor micas display a strong tendency to volume nucleation. For some specific compositions belonging to the latter group, the addition of MoO₃ and ZrO₂ has been studied. MoO₃ was selected because it is known to promote homogeneous nucleation by lowering the surface energy difference between melt and crystals, and ZrO₂ was selected because it is a classical nucleation catalyst in many glass-ceramic Systems. It is shown that both additives substantially reduce the crystallization rates and also cause concomitant changes in the resulting ceramic microstructures. Both effects are interpretated as a consequence of increased melt viscosity. An effect of nucleus formation promoted by MoO₃ is not observed.
  • Thumbnail Image
    Item
    Real group orbits on ag ind-varieties of SL (∞;C)
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2016) Ignatyev, Mikhail V.; Penkov, Ivan; Wolf, Joseph A.
    We consider the complex ind-group G=SL(∞,C) and its real forms G0=SU(∞,∞), SU(p,∞), SL(∞,R), SL(∞,H). Our main object of study are the G0-orbits on an ind-variety G/P for an arbitrary splitting parabolic ind-subgroup P⊂G, under the assumption that the subgroups G0⊂G and P⊂G are aligned in a natural way. We prove that the intersection of any G0-orbit on G/P with a finite-dimensional flag variety Gn/Pn from a given exhaustion of G/P via Gn/Pn for n→∞, is a single (G0∩Gn)-orbit. We also characterize all ind-varieties G/P on which there are finitely many G0-orbits, and provide criteria for the existence of open and close G0-orbits on G/P in the case of infinitely many G0-orbits.