Abstract:We generalize an algorithm established in earlier work [19] to compute finitely many generators for a subgroup of finite index of a group acting discontinuously on hyperbolic space of dimension 2 and 3, to hyperbolic space of higher dimensions using Clifford algebras. We hence get an algorithm which gives a finite set of generators up to finite index of a discrete subgroup of Vahlen's group, i.e. a group of 2-by-2 matrices with entries in the Clifford algebra satisfying certain conditions. The motivation comes… Show more
“…This result agrees with [29,Lemma 5.3]. There it is shown that SL + (Γ 4 (Z)) is of index four in a group, denoted SL + ( Γ4 (Z)), which is isomorphic to SL 2 (L).…”
Section: The Group E 2 (γ N (Z)) Is An Amalgamated Productsupporting
confidence: 90%
“…One of the first papers handling units in 2 × 2 matrix groups over orders in quaternion algebras is [29]. It is shown that it all comes down to studying discrete subgroups of Vahlen groups, which are 2 × 2 matrices with entries in a Clifford algebra.…”
“…This result agrees with [29,Lemma 5.3]. There it is shown that SL + (Γ 4 (Z)) is of index four in a group, denoted SL + ( Γ4 (Z)), which is isomorphic to SL 2 (L).…”
Section: The Group E 2 (γ N (Z)) Is An Amalgamated Productsupporting
confidence: 90%
“…One of the first papers handling units in 2 × 2 matrix groups over orders in quaternion algebras is [29]. It is shown that it all comes down to studying discrete subgroups of Vahlen groups, which are 2 × 2 matrices with entries in a Clifford algebra.…”
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