• Title/Summary/Keyword: p-compact groups

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HOMOTOPY FIXED POINT SETS AND ACTIONS ON HOMOGENEOUS SPACES OF p-COMPACT GROUPS

  • Kenshi Ishiguro;Lee, Hyang-Sook
    • Journal of the Korean Mathematical Society
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    • v.41 no.6
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    • pp.1101-1114
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    • 2004
  • We generalize a result of Dror Farjoun and Zabrodsky on the relationship between fixed point sets and homotopy fixed point sets, which is related to the generalized Sullivan Conjecture. As an application, we discuss extension problems considering actions on homogeneous spaces of p-compact groups.

INVARIANT RINGS AND DUAL REPRESENTATIONS OF DIHEDRAL GROUPS

  • Ishiguro, Kenshi
    • Journal of the Korean Mathematical Society
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    • v.47 no.2
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    • pp.299-309
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    • 2010
  • The Weyl group of a compact connected Lie group is a reflection group. If such Lie groups are locally isomorphic, the representations of the Weyl groups are rationally equivalent. They need not however be equivalent as integral representations. Turning to the invariant theory, the rational cohomology of a classifying space is a ring of invariants, which is a polynomial ring. In the modular case, we will ask if rings of invariants are polynomial algebras, and if each of them can be realized as the mod p cohomology of a space, particularly for dihedral groups.

Feasibility of Gamma Knife Radiosurgery for Brain Arteriovenous Malformations According to Nidus Type

  • Ja Ho Koo;Eui Hyun Hwang;Ji Hye Song;Yong Cheol Lim
    • Journal of Korean Neurosurgical Society
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    • v.67 no.4
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    • pp.431-441
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    • 2024
  • Objective : Gamma Knife radiosurgery (GKRS) is an effective and noninvasive treatment for high-risk arteriovenous malformations (AVMs). Since differences in GKRS outcomes by nidus type are unknown, this study evaluated GKRS feasibility and safety in patients with brain AVMs. Methods : This single-center retrospective study included patients with AVM who underwent GKRS between 2008 and 2021. Patients were divided into compact- and diffuse-type groups according to nidus characteristics. We excluded patients who performed GKRS and did not follow-up evaluation with magnetic resonance imaging or digital subtraction angiography within 36 months from the study. We used univariate and multivariate analyses to characterize associations of nidus type with obliteration rate and GKRS-related complications. Results : We enrolled 154 patients (mean age, 32.14±17.17 years; mean post-GKRS follow-up, 52.10±33.67 months) of whom 131 (85.1%) had compact- and 23 (14.9%) diffuse-type nidus AVMs. Of all AVMs, 89 (57.8%) were unruptured, and 65 (42.2%) had ruptured. The mean Spetzler-Martin AVM grades were 2.03±0.95 and 3.39±1.23 for the compact- and diffuse-type groups, respectively (p<0.001). During the follow-up period, AVM-related hemorrhages occurred in four individuals (2.6%), three of whom had compact nidi. Substantial radiation-induced changes and cyst formation were observed in 21 (13.6%) and one patient (0.6%), respectively. The AVM complete obliteration rate was 46.1% across both groups. Post-GKRS complication and complete obliteration rates were not significantly different between nidus types. For diffuse-type nidus AVMs, larger AVM size and volume (p<0.001), lower radiation dose (p<0.001), eloquent area location (p=0.015), and higher Spetzler-Martin grade (p<0.001) were observed. Conclusion : GKRS is a safe and feasible treatment for brain AVMs characterized by both diffuse- and compact-type nidi.

MODULAR INVARIANTS UNDER THE ACTIONS OF SOME REFLECTION GROUPS RELATED TO WEYL GROUPS

  • Ishiguro, Kenshi;Koba, Takahiro;Miyauchi, Toshiyuki;Takigawa, Erika
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.1
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    • pp.207-218
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    • 2020
  • Some modular representations of reflection groups related to Weyl groups are considered. The rational cohomology of the classifying space of a compact connected Lie group G with a maximal torus T is expressed as the ring of invariants, H*(BG; ℚ) ≅ H*(BT; ℚ)W(G), which is a polynomial ring. If such Lie groups are locally isomorphic, the rational representations of their Weyl groups are equivalent. However, the integral representations need not be equivalent. Under the mod p reductions, we consider the structure of the rings, particularly for the Weyl group of symplectic groups Sp(n) and for the alternating groups An as the subgroup of W(SU(n)). We will ask if such rings of invariants are polynomial rings, and if each of them can be realized as the mod p cohomology of a space. For n = 3, 4, the rings under a conjugate of W(Sp(n)) are shown to be polynomial, and for n = 6, 8, they are non-polynomial. The structures of H*(BTn-1; 𝔽p)An will be also discussed for n = 3, 4.

TORSION IN THE HOMOLOGY OF THE DOUBLE LOOP SPACES OF COMPACT SIMPLE LIE GROUPS

  • Choi, Young-Gi;Yoon, Seong-Hee
    • Journal of the Korean Mathematical Society
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    • v.39 no.1
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    • pp.149-161
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    • 2002
  • We study the torsions in the integral homology of the double loop space of the compact simple Lie groups by determining the higher Bockstein actions on the homology of those spaces through the Bockstein lemma and computing the Bockstein spectral sequence.

A COMPARATIVE STUDY ON THE MECHANICAL PROPERTIES OF CONDENSABLE COMPOSITE RESINS (응축형 복합레진의 기계적 성질에 관한 비교연구)

  • 정지아;문주훈;조영곤
    • Restorative Dentistry and Endodontics
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    • v.26 no.6
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    • pp.485-491
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    • 2001
  • The purpose of this study was to compare the mechanical properties of three condensable composite resins and one hybrid composite resin. The compressive strength, diametral tensile strength, Vicker's microhardness were tested for mechanical properties of condensable composite resins (SureFil, Ariston pHc, Synergy compact), and hybrid composite resin (Z 100). The tested materials were divided into four groups: control group Z 100 (3M Co. USA), experimental group I Ariston pHc, (Vivadent, Co., Liechtenstein) experimental group II SureFil (Dentsply, Co., U.S.A.), experimental group III Synergy Compact (Coltene, Co., Swiss). According to the above classification, we made samples of SureFil, Ariston pHc, Synergy Compact, Z 100 with separable cylindrical metal mold. And then, we measured and compared the value of compressive strength, diametral tensile strength and Vicker's microhardness of each sample. (omitted)

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TOTALLY DISCONNECTED GROUPS, P-ADIC GROUPS AND THE HILBERT-SMITH CONJECTURE

  • Lee, Joo-Sung
    • Communications of the Korean Mathematical Society
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    • v.12 no.3
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    • pp.691-699
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    • 1997
  • The following statement is known as the generalized Hilbert-Smith conjecture : If G is a compact group and acts effectively on a manifold, then G is a Lie group. In this paper we prove that the generalized Hilbert-Smith conjecture is equivalent to the following : A known, but has never been published before.

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INVARIANT RINGS AND REPRESENTATIONS OF SYMMETRIC GROUPS

  • Kudo, Shotaro
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.4
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    • pp.1193-1200
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    • 2013
  • The center of the Lie group $SU(n)$ is isomorphic to $\mathbb{Z}_n$. If $d$ divides $n$, the quotient $SU(n)/\mathbb{Z}_d$ is also a Lie group. Such groups are locally isomorphic, and their Weyl groups $W(SU(n)/\mathbb{Z}_d)$ are the symmetric group ${\sum}_n$. However, the integral representations of the Weyl groups are not equivalent. Under the mod $p$ reductions, we consider the structure of invariant rings $H^*(BT^{n-1};\mathbb{F}_p)^W$ for $W=W(SU(n)/\mathbb{Z}_d)$. Particularly, we ask if each of them is a polynomial ring. Our results show some polynomial and non-polynomial cases.