Determining Maximal Orders of a Quaternion Algebra
1
$begingroup$
Let $F=left(frac{a,b}{K}right)$ be a quaternion algebra for some number field $K$. What method do we use to determine a maximal order of $F$ (or the class of maximal orders of $F$)?
number-theory algebraic-number-theory quaternions
asked Nov 30 '18 at 17:50
ChrisChris
332112
$endgroup$
add a comment |
1
$begingroup$
Let $F=left(frac{a,b}{K}right)$ be a quaternion algebra for some number field $K$. What method do we use to determine a maximal order of $F$ (or the class of maximal orders of $F$)?
number-theory algebraic-number-theory quaternions
asked Nov 30 '18 at 17:50
ChrisChris
332112
$endgroup$
$begingroup$
Ivanyos and Rónyai have published an algorithm for handling this task. IIRC it is implemented in at least MAGMA. I do recall that implementation running out of mem when we tried to use it on a large cyclic algebra. We managed to use the ideas and known special facts about our case to find a maximal order. I'm afraid the details have mostly faded from my mind even though I was in charge of that part of our joint paper.
$endgroup$
– Jyrki Lahtonen
Dec 1 '18 at 18:03
$begingroup$
The idea was to build orders mapping a suitable lattice to itself. I & R had a useful way of alternately increasing the lattice and the related order alternately, but I don't remember any of the details.
$endgroup$
– Jyrki Lahtonen
Dec 1 '18 at 18:08
add a comment |
1
1
1
$begingroup$
Let $F=left(frac{a,b}{K}right)$ be a quaternion algebra for some number field $K$. What method do we use to determine a maximal order of $F$ (or the class of maximal orders of $F$)?
number-theory algebraic-number-theory quaternions
asked Nov 30 '18 at 17:50
ChrisChris
332112
$endgroup$
Let $F=left(frac{a,b}{K}right)$ be a quaternion algebra for some number field $K$. What method do we use to determine a maximal order of $F$ (or the class of maximal orders of $F$)?
number-theory algebraic-number-theory quaternions
number-theory algebraic-number-theory quaternions
asked Nov 30 '18 at 17:50
ChrisChris
332112
asked Nov 30 '18 at 17:50
ChrisChris
332112
asked Nov 30 '18 at 17:50
ChrisChris
332112
asked Nov 30 '18 at 17:50
ChrisChris
332112
asked Nov 30 '18 at 17:50
ChrisChris
332112
332112
$begingroup$
Ivanyos and Rónyai have published an algorithm for handling this task. IIRC it is implemented in at least MAGMA. I do recall that implementation running out of mem when we tried to use it on a large cyclic algebra. We managed to use the ideas and known special facts about our case to find a maximal order. I'm afraid the details have mostly faded from my mind even though I was in charge of that part of our joint paper.
$endgroup$
– Jyrki Lahtonen
Dec 1 '18 at 18:03
$begingroup$
The idea was to build orders mapping a suitable lattice to itself. I & R had a useful way of alternately increasing the lattice and the related order alternately, but I don't remember any of the details.
$endgroup$
– Jyrki Lahtonen
Dec 1 '18 at 18:08
add a comment |
$begingroup$
Ivanyos and Rónyai have published an algorithm for handling this task. IIRC it is implemented in at least MAGMA. I do recall that implementation running out of mem when we tried to use it on a large cyclic algebra. We managed to use the ideas and known special facts about our case to find a maximal order. I'm afraid the details have mostly faded from my mind even though I was in charge of that part of our joint paper.
$endgroup$
– Jyrki Lahtonen
Dec 1 '18 at 18:03
$begingroup$
The idea was to build orders mapping a suitable lattice to itself. I & R had a useful way of alternately increasing the lattice and the related order alternately, but I don't remember any of the details.
$endgroup$
– Jyrki Lahtonen
Dec 1 '18 at 18:08
$begingroup$
Ivanyos and Rónyai have published an algorithm for handling this task. IIRC it is implemented in at least MAGMA. I do recall that implementation running out of mem when we tried to use it on a large cyclic algebra. We managed to use the ideas and known special facts about our case to find a maximal order. I'm afraid the details have mostly faded from my mind even though I was in charge of that part of our joint paper.
$endgroup$
– Jyrki Lahtonen
Dec 1 '18 at 18:03
$begingroup$
Ivanyos and Rónyai have published an algorithm for handling this task. IIRC it is implemented in at least MAGMA. I do recall that implementation running out of mem when we tried to use it on a large cyclic algebra. We managed to use the ideas and known special facts about our case to find a maximal order. I'm afraid the details have mostly faded from my mind even though I was in charge of that part of our joint paper.
$endgroup$
– Jyrki Lahtonen
Dec 1 '18 at 18:03
$begingroup$
The idea was to build orders mapping a suitable lattice to itself. I & R had a useful way of alternately increasing the lattice and the related order alternately, but I don't remember any of the details.
$endgroup$
– Jyrki Lahtonen
Dec 1 '18 at 18:08
$begingroup$
The idea was to build orders mapping a suitable lattice to itself. I & R had a useful way of alternately increasing the lattice and the related order alternately, but I don't remember any of the details.
$endgroup$
– Jyrki Lahtonen
Dec 1 '18 at 18:08
add a comment |
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$begingroup$
Ivanyos and Rónyai have published an algorithm for handling this task. IIRC it is implemented in at least MAGMA. I do recall that implementation running out of mem when we tried to use it on a large cyclic algebra. We managed to use the ideas and known special facts about our case to find a maximal order. I'm afraid the details have mostly faded from my mind even though I was in charge of that part of our joint paper.
$endgroup$
– Jyrki Lahtonen
Dec 1 '18 at 18:03
$begingroup$
The idea was to build orders mapping a suitable lattice to itself. I & R had a useful way of alternately increasing the lattice and the related order alternately, but I don't remember any of the details.
$endgroup$
– Jyrki Lahtonen
Dec 1 '18 at 18:08