Commuting isometries of the complex hyperbolic space
نویسندگان
چکیده
منابع مشابه
Algebraic Characterization of the Isometries of the Hyperbolic 5-space
Abstract. Let GL(2,H) be the group of invertible 2 × 2 matrices over the division algebra H of quaternions. GL(2,H) acts on the hyperbolic 5-space as the group of orientation-preserving isometries. Using this action we give an algebraic characterization of the dynamical types of the orientation-preserving isometries of the hyperbolic 5-space. Along the way we also determine the conjugacy classe...
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Let G be a group. Two elements x, y are said to be z-equivalent if their centralizers are conjugate in G. The class equation of G is the partition of G into conjugacy classes. Further decomposition of conjugacy classes into z-classes provides an important information about the internal structure of the group, cf. [8] for the elaboration of this theme. Let I(Hn) denote the group of isometries of...
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In this paper after giving a finer classification, we give an algebraic characterization of the dynamical types of the isometries of the hyperbolic n-space H. This has been done by using the linear representation of the isometry group in the hyperboloid model of H. Using the representation of the isometries as 2× 2 matrices over C and H, we give another algebraic characterization of the dynamic...
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In this paper we give a finer classification of the dynamical types of the orientationpreserving isometries of the hyperbolic 5-space and characterize them algebraically. We also derive the parameter spaces of isometries of fixed dynamical type.
متن کاملIsometries of the Hyperbolic Plane
In this paper, I will explore basic properties of the group PSL(2,R). These include the relationship between isometries of H2, Möbius transformations, and matrix multiplication. In addition, this paper will explain a method of characterizing the aforementioned transformations by the trace of their matrices through looking at the number of xed points of a transformation.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2011
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2011-10796-2