TY - JOUR
T1 - Structure and equivalence of a class of tube domains with solvable groups of automorphisms
AU - Shimizu, Satoru
N1 - Funding Information:
This work was partly supported by the Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science.
Publisher Copyright:
© 2017 The Mathematical Society of Japan.
PY - 2017
Y1 - 2017
N2 - In the study of the holomorphic equivalence problem for tube domains, it is fundamental to investigate tube domains with polynomial infinitesimal automorphisms. To apply Lie group theory to the holomorphic equivalence problem for such tube domains TΩ, investigating certain solvable subalgebras of g(Ω) plays an important role, where g(Ω) is the Lie algebra of all complete polynomial vector fields on Ω. Related to this theme, we discuss in this paper the structure and equivalence of a class of tube domains with solvable groups of automorphisms. Besides, we give a concrete example of a tube domain whose automorphism group is solvable and contains nonaffine automorphisms.
AB - In the study of the holomorphic equivalence problem for tube domains, it is fundamental to investigate tube domains with polynomial infinitesimal automorphisms. To apply Lie group theory to the holomorphic equivalence problem for such tube domains TΩ, investigating certain solvable subalgebras of g(Ω) plays an important role, where g(Ω) is the Lie algebra of all complete polynomial vector fields on Ω. Related to this theme, we discuss in this paper the structure and equivalence of a class of tube domains with solvable groups of automorphisms. Besides, we give a concrete example of a tube domain whose automorphism group is solvable and contains nonaffine automorphisms.
KW - Holomorphic equivalence problem
KW - Solvable groups
KW - Tube domains
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U2 - 10.2969/jmsj/06931157
DO - 10.2969/jmsj/06931157
M3 - Article
AN - SCOPUS:85026892586
VL - 69
SP - 1157
EP - 1177
JO - Journal of the Mathematical Society of Japan
JF - Journal of the Mathematical Society of Japan
SN - 0025-5645
IS - 3
ER -