Spinor genus Contents Definitions Results See also References Navigation menu0395.100290915.52003

Quadratic forms


quadratic formsring of integersMartin Eichlergenusquadratic spacespinor normequivalence relationindefinite forms




In mathematics, the spinor genus is a classification of quadratic forms and lattices over the ring of integers, introduced by Martin Eichler. It refines the genus but may be coarser than proper equivalence




Contents





  • 1 Definitions


  • 2 Results


  • 3 See also


  • 4 References




Definitions


We define two Z-lattices L and M in a quadratic space V over Q to be spinor equivalent if there exists a transformation g in the proper orthogonal group O+(V) and for every prime p there exists a local transformation fp of Vp of spinor norm 1 such that M = g fpLp.


A spinor genus is an equivalence class for this equivalence relation. Properly equivalent lattices are in the same spinor genus, and lattices in the same spinor genus are in the same genus. The number of spinor genera in a genus is a power of two, and can be determined effectively.



Results


An important result is that for indefinite forms of dimension at least three, each spinor genus contains exactly one proper equivalence class.



See also


  • Genus of a quadratic form


References



  • Cassels, J. W. S. (1978). Rational Quadratic Forms. London Mathematical Society Monographs. 13. Academic Press. ISBN 0-12-163260-1. Zbl 0395.10029..mw-parser-output cite.citationfont-style:inherit.mw-parser-output .citation qquotes:"""""""'""'".mw-parser-output .citation .cs1-lock-free abackground:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration abackground:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center.mw-parser-output .citation .cs1-lock-subscription abackground:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registrationcolor:#555.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration spanborder-bottom:1px dotted;cursor:help.mw-parser-output .cs1-ws-icon abackground:url("//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png")no-repeat;background-position:right .1em center.mw-parser-output code.cs1-codecolor:inherit;background:inherit;border:inherit;padding:inherit.mw-parser-output .cs1-hidden-errordisplay:none;font-size:100%.mw-parser-output .cs1-visible-errorfont-size:100%.mw-parser-output .cs1-maintdisplay:none;color:#33aa33;margin-left:0.3em.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-formatfont-size:95%.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-leftpadding-left:0.2em.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-rightpadding-right:0.2em


  • Conway, J. H.; Sloane, N. J. A. Sphere packings, lattices and groups. Grundlehren der Mathematischen Wissenschaften. 290. With contributions by Bannai, E.; Borcherds, R. E.; Leech, J.; Norton, S. P.; Odlyzko, A. M.; Parker, R. A.; Queen, L.; Venkov, B. B. (3rd ed.). New York, NY: Springer-Verlag. ISBN 0-387-98585-9. Zbl 0915.52003.


-

Popular posts from this blog

Thal And Out Agency railway station See also References External links Navigation menuOfficial Web Site of Pakistan RailwaysArchivedOfficial Web Site of Pakistan Railwayseeexpanding ite

Image
Golra Sharif KutbalFatehjangGaganChauntraKahal Basal Junction DomelNammalChura Sharif HaltLangar Jand Junction Khushalgarh Faqir Hussain ShaheedTilkanSeni GambatBabari BandaCadet College Kohat Kohat Cantonment Kohat Tehsil Nasrat Khel Chikarkot Ustarzai Raisan Ibrahimzai Hangu Doaba Darsmand Thal Aab-e-gumAhmedwalAlam RegAlozaiAzadBadinzaiBakhtiarabad DomkiBeleli Bostan Junction Chaman ChurmianDalbandinDamboliDera Allah YarDera Murad JamaliDingraDozanGalangurGatGulistanHirokKan MehtarzaiKhanaiKhan Muhammad ChahKila SaifullahKishingiKoh-e-TaftanKolpurKuchlakMachMangoliMirjavehMushkafMuslimbaghNok KundiNushkiNuttallPadag RoadPerakPehro KunriPanirPeshiQilla Abdullah Quetta Sar-i-AbSheikh MandahSheikh Wasil Sibi Junction Spezand Junction Shela BaghTozghiWali KhanYakmachYaru Zhob IslamabadGolra Sharif Junction Attock City Junction Attock KhurdBahawalpurChiniotDandot RSFaisalabadGujar KhanGujratJalloJhang SadarJhelum Khanewal Junction KhanpurKhewra Lahore Junction Lahore CantonmentLiaquat Pu...
Read more

Posting a File and Associated Data to a RESTful WebService preferably as JSON2019 Community Moderator ElectionREST URI convention - Singular or plural name of resource while creating itUploading both data and files in one form using Ajax?How do I upload a file with metadata using a REST web service?REST API - file (ie images) processing - best practicesSpring: JSON data and file in the same requestREST API Put large dataPosting a file and JSON data to Spring rest serviceRESTful Web Service Upload/Download Large Data With JSONREST API Design sending JSON data and a file to the api in same requestPost JSONArray to REST servicePUT vs. POST in RESTParsing values from a JSON file?JavaScript/jQuery to download file via POST with JSON dataHow do I upload a file with metadata using a REST web service?How to POST JSON data with Curl from Terminal/Commandline to Test Spring REST?Separate REST JSON API server and client?what's the correct way to send a file from REST web service to client?How do I write JSON data to a file?What is “406-Not Acceptable Response” in HTTP?REST API - file (ie images) processing - best practices

Image
Convert an array of objects to array of the objects' values Can a space-faring robot still function over a billion years? ESPP--any reason not to go all in? Create chunks from an array Has a sovereign Communist government ever run, and conceded loss, on a fair election? When to use the term transposed instead of modulation? How to chmod files that have a specific set of permissions Is this nominative case or accusative case? Are there other characters in the Star Wars universe who had damaged bodies and needed to wear an outfit like Darth Vader? What does "rhumatis" mean? How to write a chaotic neutral protagonist and prevent my readers from thinking they are evil? Can a Mimic (container form) actually hold loot? A bug in Excel? Conditional formatting for marking duplicates also highlights unique value What is Tony Stark injecting into himself in Iron Man 3? Iron deposits mined from under the city Why would the IRS ask for birth certificates ...
Read more

How can I change the color of pagination dots of UIPageControl?How to change UIPageControl dotsIs there a way to change page indicator dots colorCustomize dot with image of UIPageControl at index 0 of UIPageControlNo visible @interface for 'NSObject<PageControlDelegate>' declares the selector 'pageControlPageDidChange:'How to change the color of pagination dots in UIPageControl with a different color per pagepagecontrol indicator custom image instead of DefaultChanging the colour of UIPageControl dots in MonoTouchpagecontrol selectable page visibility color?Alternative way to load ViewControllers on a UIPageControlHow to set only layer.border-color for UIpage control dots in swiftHow can I develop for iPhone using a Windows development machine?How to change the name of an iOS app?UITableView - change section header coloruipagecontrol indicator(dot)issueCustom UIPageControl dots color not changingchange the interspace between UIPageControl dotsHow to change Status Bar text color in iOSHow can I change image tintColor in iOS and WatchKitUIPageControl dots with larger space in between each dotsHow to change the color of pagination dots in UIPageControl with a different color per page

Image
How do I implement a file system driver driver in Linux? Fly on a jet pack vs fly with a jet pack? Is possible to search in vim history? Translation of Scottish 16th century church stained glass Ridge Regression with Gradient Descent Converges to OLS estimates What linear sensor for a keyboard? Did US corporations pay demonstrators in the German demonstrations against article 13? Is it improper etiquette to ask your opponent what his/her rating is before the game? Why does Async/Await work properly when the loop is inside the async function and not the other way around? Why did the EU agree to delay the Brexit deadline? A Permanent Norse Presence in America Did arcade monitors have same pixel aspect ratio as TV sets? Can the Supreme Court overturn an impeachment? Drawing ramified coverings with tikz Greco-Roman egalitarianism Can someone explain how this makes sense electrically? Is it possible to use .desktop files to open local pdf files on specific pa...
Read more