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

Understanding generators in Python2019 Community Moderator ElectionGenerator function not working pythonFor loop not executing two timesGenerators - Printing generated valuesWhy can a python generator only be used once?What exactly do generators do?What does the “yield” keyword do?What does “list comprehension” mean? How does it work and how can I use it?sklearn Kfold acces single fold instead of for loopIs a generator the callable? Which is the generator?Apply Border To Range Of Cells Using OpenpyxlCalling an external command in PythonWhat are metaclasses in Python?What is the difference between @staticmethod and @classmethod?Finding the index of an item given a list containing it in PythonDifference between append vs. extend list methods in PythonHow can I safely create a nested directory in Python?Does Python have a ternary conditional operator?Understanding slice notationUnderstanding Python super() with __init__() methodsDoes Python have a string 'contains' substring method?

Image
What is it called when someone votes for an option that's not their first choice? Have the tides ever turned twice on any open problem? Is xar preinstalled on macOS? "Marked down as someone wanting to sell shares." What does that mean? Does fire aspect on a sword, destroy mob drops? Is VPN a layer 3 concept? Exposing a company lying about themselves in a tightly knit industry: Is my career at risk on the long run? Symbolism of 18 Journeyers How can a new country break out from a developed country without war? What is the difference between something being completely legal and being completely decriminalized? Does convergence of polynomials imply that of its coefficients? Friend wants my recommendation but I don't want to give it to him Why I don't get the wanted width of tcbox? Single word to change groups Would this string work as string? Unfrosted light bulb Air travel with refrigerated insulin What is the tangent at a sharp poi...
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