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Classifying integral crystallographi...

Sheydvasser, Arseniy.

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Classifying integral crystallographic packings.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Classifying integral crystallographic packings./
Author:	Sheydvasser, Arseniy.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2018,
Description:	100 p.
Notes:	Source: Dissertations Abstracts International, Volume: 80-02, Section: B.
Contained By:	Dissertations Abstracts International80-02B.
Subject:	Theoretical Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10927908
ISBN:	9780438194786

Classifying integral crystallographic packings.
Sheydvasser, Arseniy.

Classifying integral crystallographic packings. - Ann Arbor : ProQuest Dissertations & Theses, 2018 - 100 p.

Source: Dissertations Abstracts International, Volume: 80-02, Section: B.

Thesis (Ph.D.)--Yale University, 2018.

This item must not be added to any third party search indexes.

We give a procedure of constructing analogs of the Apollonian circle packing known as integral crystallographic sphere packings. Our approach uses the notion of maximal orders over quaternion algebras with orthogonal involution, which was originally studied by Scharlau in the 1970s. We give a classification of such orders over local and global fields. Over local fields, we show that there is a correspondence between maximal and/or modular lattices and orders closed under the involution. Using this machinery, we define an analog of Bianchi groups for rational quaternion algebras and use it to construct analogs of the superpacking of the Apollonian circle packing. Finally, we show how to produce integral crystallographic packings from candidate superpackings.

ISBN: 9780438194786Subjects--Topical Terms:

1672766
Theoretical Mathematics.

Classifying integral crystallographic packings.
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020 $a 9780438194786
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100 1 $a Sheydvasser, Arseniy. $3 3437669
245 1 0 $a Classifying integral crystallographic packings.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2018
300 $a 100 p.
500 $a Source: Dissertations Abstracts International, Volume: 80-02, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Kontorovich, Alexander.
502 $a Thesis (Ph.D.)--Yale University, 2018.
506 $a This item must not be added to any third party search indexes.
506 $a This item must not be sold to any third party vendors.
520 $a We give a procedure of constructing analogs of the Apollonian circle packing known as integral crystallographic sphere packings. Our approach uses the notion of maximal orders over quaternion algebras with orthogonal involution, which was originally studied by Scharlau in the 1970s. We give a classification of such orders over local and global fields. Over local fields, we show that there is a correspondence between maximal and/or modular lattices and orders closed under the involution. Using this machinery, we define an analog of Bianchi groups for rational quaternion algebras and use it to construct analogs of the superpacking of the Apollonian circle packing. Finally, we show how to produce integral crystallographic packings from candidate superpackings.
590 $a School code: 0265.
650 4 $a Theoretical Mathematics. $3 1672766
690 $a 0642
710 2 $a Yale University. $3 515640
773 0 $t Dissertations Abstracts International $g 80-02B.
790 $a 0265
791 $a Ph.D.
792 $a 2018
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10927908