# On roots of the automorphism group of a circular domain in ${\u2102}^{n}$

Annales Polonici Mathematici (1991)

- Volume: 55, Issue: 1, page 269-276
- ISSN: 0066-2216

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topJan M. Myszewski. "On roots of the automorphism group of a circular domain in $ℂ^n$." Annales Polonici Mathematici 55.1 (1991): 269-276. <http://eudml.org/doc/262279>.

@article{JanM1991,

abstract = {We study the properties of the group Aut(D) of all biholomorphic transformations of a bounded circular domain D in $ℂ^n$ containing the origin. We characterize the set of all possible roots for the Lie algebra of Aut(D). There exists an n-element set P such that any root is of the form α or -α or α-β for suitable α,β ∈ P.},

author = {Jan M. Myszewski},

journal = {Annales Polonici Mathematici},

keywords = {circular domain; automorphism group; maximal torus; Lie algebra; adjoint representation; root; root subspace; bounded circular domain in ; Lie algebras of real vector fields},

language = {eng},

number = {1},

pages = {269-276},

title = {On roots of the automorphism group of a circular domain in $ℂ^n$},

url = {http://eudml.org/doc/262279},

volume = {55},

year = {1991},

}

TY - JOUR

AU - Jan M. Myszewski

TI - On roots of the automorphism group of a circular domain in $ℂ^n$

JO - Annales Polonici Mathematici

PY - 1991

VL - 55

IS - 1

SP - 269

EP - 276

AB - We study the properties of the group Aut(D) of all biholomorphic transformations of a bounded circular domain D in $ℂ^n$ containing the origin. We characterize the set of all possible roots for the Lie algebra of Aut(D). There exists an n-element set P such that any root is of the form α or -α or α-β for suitable α,β ∈ P.

LA - eng

KW - circular domain; automorphism group; maximal torus; Lie algebra; adjoint representation; root; root subspace; bounded circular domain in ; Lie algebras of real vector fields

UR - http://eudml.org/doc/262279

ER -

## References

top- [1] J. F. Adams, Lectures on Lie Groups, Benjamin, New York 1969. Zbl0206.31604
- [2] W. Kaup and H. Upmeier, Banach spaces with biholomorphically equivalent balls are isomorphic, Proc. Amer. Math. Soc. 58 (1976), 129-133. Zbl0337.32012
- [3] J. M. Myszewski, On maximal tori of the automorphism group of circular domain in ${\u2102}^{n}$, Demonstratio Math. 22 (4) (1989), 1067-1080. Zbl0765.32001
- [4] R. Narasimhan, Several Complex Variables, Chicago Lectures in Mathematics, The University of Chicago Press, Chicago & London 1971. Zbl0223.32001
- [5] T. Sunada, Holomorphic equivalence problem for bounded Reinhardt domains, Math. Ann. 235 (1978), 111-128. Zbl0357.32001

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