• Title, Summary, Keyword: automorphism group

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NEW AND OLD RESULTS OF COMPUTATIONS OF AUTOMORPHISM GROUP OF DOMAINS IN THE COMPLEX SPACE

  • Byun, Jisoo
    • East Asian mathematical journal
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    • v.31 no.3
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    • pp.363-370
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    • 2015
  • The automorphism group of domains is main stream of classification problem coming from E. Cartan's work. In this paper, I introduce classical technique of computations of automorphism group of domains and recent development of automorphism group. Moreover, I suggest new research problems in computations of automorphism group.

PERTURBATION OF DOMAINS AND AUTOMORPHISM GROUPS

  • Fridman, Buma L.;Ma, Daowei
    • Journal of the Korean Mathematical Society
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    • v.40 no.3
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    • pp.487-501
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    • 2003
  • The paper is devoted to the description of changes of the structure of the holomorphic automorphism group of a bounded domain in \mathbb{C}^n under small perturbation of this domain in the Hausdorff metric. We consider a number of examples when an arbitrary small perturbation can lead to a domain with a larger group, present theorems concerning upper semicontinuity property of some invariants of automorphism groups. We also prove that the dimension of an abelian subgroup of the automorphism group of a bounded domain in \mathbb{C}^n does not exceed n.

REPRESENTATIONS OF THE AUTOMORPHISM GROUP OF A SUPERSINGULAR K3 SURFACE OF ARTIN-INVARIANT 1 OVER ODD CHARACTERISTIC

  • Jang, Junmyeong
    • Journal of the Chungcheong Mathematical Society
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    • v.27 no.2
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    • pp.287-295
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    • 2014
  • In this paper, we prove that the image of the representation of the automorphism group of a supersingular K3 surface of Artin-invariant 1 over odd characteristic p on the global two forms is a finite cyclic group of order p + 1. Using this result, we deduce, for such a K3 surface, there exists an automorphism which cannot be lifted over a field of characteristic 0.

Code automorphism group algorithms and applications

  • Cho, Han-Hyuk;Shin, Hye-Sun;Yeo, Tae-Kyung
    • Communications of the Korean Mathematical Society
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    • v.11 no.3
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    • pp.575-584
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    • 1996
  • We investigate how the code automorphism groups can be used to study such combinatorial objects as codes, finite projective planes and Hadamard matrices. For this purpose, we write down a computer program for computing code automorphisms in PASCAL language. Then we study the combinatorial properties using those code automorphism group algorithms and the relationship between combinatorial objects and codes.

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GENERALIZED CAYLEY GRAPHS OF RECTANGULAR GROUPS

  • ZHU, YONGWEN
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.4
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    • pp.1169-1183
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    • 2015
  • We describe generalized Cayley graphs of rectangular groups, so that we obtain (1) an equivalent condition for two Cayley graphs of a rectangular group to be isomorphic to each other, (2) a necessary and sufficient condition for a generalized Cayley graph of a rectangular group to be (strong) connected, (3) a necessary and sufficient condition for the colour-preserving automorphism group of such a graph to be vertex-transitive, and (4) a sufficient condition for the automorphism group of such a graph to be vertex-transitive.

CHARACTERIZATION OF REINHARDT DOMAINS BY THEIR AUTOMORPHISM GROUPS

  • Isaen, Alexander-V.;Krantz, Steven-G.
    • Journal of the Korean Mathematical Society
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    • v.37 no.2
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    • pp.297-308
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    • 2000
  • We survey results, obtained in the past three years, on characterizing bounded (and Kobayashi-hyperbolic) Reinhardt domains by their automorphism groups. Specifically, we consider the following two situations: (i) the group is non-compact, and (ii) the dimension of the group is sufficiently large. In addition, we prove two theorems on characterizing general hyperbolic complex manifolds by the dimensions of their automorphism groups.

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