Krishnendu Gongopadhyay
On the Conjugacy Classes in the orthogonal and symplectic groups over algebraically closed fields.
Tue, 11/03/2009 - 16:01 — SomNambulAuthors: Krishnendu Gongopadhyay
Subjects: Group Theory
AbstractLet $\F$ be an algebraically closed field. Let $\V$ be a vector space
equipped with a non-degenerate symmetric or symplectic bilinear form $B$ over
$\F$. Suppose the characteristic of $\F$ is \emph{large}, i.e. either zero or
greater than the dimension of $\V$. Let $I(\V, B)$ denote the group of
isometries. Using the Jacobson-Morozov lemma we give a new and simple proof of
the fact that two elements in $I(\V,B)$ are conjugate if and only if they have
the same elementary divisors.Topology of the conjugacy classes in Moebius groups.
Tue, 10/13/2009 - 18:46 — SomNambulAuthors: Krishnendu Gongopadhyay
Subjects: Geometric Topology
AbstractLet $H^{n+1}$ denote the $n + 1$-dimensional (real) hyperbolic space. Let
$S^n$ denote the conformal boundary of the hyperbolic space. The group of
conformal diffeomorphisms of $S^n$ is denoted by M(n). Let $M_o(n)$ be its
identity component which consists of all orientation-preserving elements in
M(n). The conjugacy classification of isometries in $M_o(n)$ depends on the
conjugacy of $T$ and $T^{-1}$ in $M_o(n)$. For an element $T$ in M(n), $T$ and
$T^{-1}$ are conjugate in M(n), but they may not be conjugate in $M_o(n)$.Algebraic Characterization of the Isometries of the Complex and Quaternionic Hyperbolic Plane.
Tue, 09/08/2009 - 12:16 — SomNambulAuthors: Wensheng Cao, Krishnendu Gongopadhyay
Subjects: Geometric Topology
AbstractLet $\F$ denote either of $\R$, $\C$ or the quaternions $\H$. Let $H^2_{\F}$
denote the two dimensional hyperbolic space over $\F$. The algebraic
characterization of the isometries of $H^2_{\R}$ and $H^3_{\R}$ in terms of
their trace and determinant are foundational in the real hyperbolic geometry.
The counterpart of this characterization for isometries of $H^2_{\C}$ was given
by Giraud and Goldman. In this paper we offer algebraic characterization for
the isometries of $H^2_{\H}$.Algebraic Characterization of the Isometries of the Complex and Quaternionic Hyperbolic Plane.
Tue, 09/08/2009 - 12:16 — SomNambulAuthors: Wensheng Cao, Krishnendu Gongopadhyay
Subjects: Geometric Topology
AbstractLet $\F$ denote either of $\R$, $\C$ or the quaternions $\H$. Let $H^2_{\F}$
denote the two dimensional hyperbolic space over $\F$. The algebraic
characterization of the isometries of $H^2_{\R}$ and $H^3_{\R}$ in terms of
their trace and determinant are foundational in the real hyperbolic geometry.
The counterpart of this characterization for isometries of $H^2_{\C}$ was given
by Giraud and Goldman. In this paper we offer algebraic characterization for
the isometries of $H^2_{\H}$.
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