FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2000592162> ?p ?o ?g. }

• W2000592162 abstract "Let <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=k> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=application/x-tex>k</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a field of characteristic different from 2 and 3. The main aim of this paper is to prove the Tits-Weiss conjecture for Albert division algebras over <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=k> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=application/x-tex>k</mml:annotation> </mml:semantics> </mml:math> </inline-formula> which are <italic>pure</italic> first Tits constructions. The conjecture asserts that, for an Albert division algebra <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=application/x-tex>A</mml:annotation> </mml:semantics> </mml:math> </inline-formula> over a field <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=k> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=application/x-tex>k</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, the structure group <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper S t r left-parenthesis upper A right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>S</mml:mi> <mml:mi>t</mml:mi> <mml:mi>r</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>A</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>Str(A)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is generated by <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper U> <mml:semantics> <mml:mi>U</mml:mi> <mml:annotation encoding=application/x-tex>U</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-operators and scalar multiplications. The conjecture derives its importance from its connections with algebraic groups and Tits buildings, particularly with Moufang polygons. It is known that <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=k> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=application/x-tex>k</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-forms of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper E 8> <mml:semantics> <mml:msub> <mml:mi>E</mml:mi> <mml:mn>8</mml:mn> </mml:msub> <mml:annotation encoding=application/x-tex>E_8</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with index <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper E Subscript 8 comma 2 Superscript 78> <mml:semantics> <mml:msubsup> <mml:mi>E</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mn>8</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mn>78</mml:mn> </mml:mrow> </mml:msubsup> <mml:annotation encoding=application/x-tex>E^{78}_{8,2}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and anisotropic kernel a strict inner <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=k> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=application/x-tex>k</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-form of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper E 6> <mml:semantics> <mml:msub> <mml:mi>E</mml:mi> <mml:mn>6</mml:mn> </mml:msub> <mml:annotation encoding=application/x-tex>E_6</mml:annotation> </mml:semantics> </mml:math> </inline-formula> correspond bijectively (via Moufang hexagons) to Albert division algebras over <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=k> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=application/x-tex>k</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. The Kneser-Tits problem for a form of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper E 8> <mml:semantics> <mml:msub> <mml:mi>E</mml:mi> <mml:mn>8</mml:mn> </mml:msub> <mml:annotation encoding=application/x-tex>E_8</mml:annotation> </mml:semantics> </mml:math> </inline-formula> as above is equivalent to the Tits-Weiss conjecture (see Section 3). We provide a solution to the Kneser-Tits problem for <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=k> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=application/x-tex>k</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-forms of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper E 8> <mml:semantics> <mml:msub> <mml:mi>E</mml:mi> <mml:mn>8</mml:mn> </mml:msub> <mml:annotation encoding=application/x-tex>E_8</mml:annotation> </mml:semantics> </mml:math> </inline-formula> corresponding to pure first Tits construction Albert division algebras. As an application, we prove that for the <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=k> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=application/x-tex>k</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-group <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G equals bold Aut left-parenthesis upper A right-parenthesis comma upper G left-parenthesis k right-parenthesis slash upper R equals 1> <mml:semantics> <mml:mrow> <mml:mi>G</mml:mi> <mml:mo>=</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mtext mathvariant=bold>Aut</mml:mtext> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>A</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>,</mml:mo> <mml:mtext> </mml:mtext> <mml:mi>G</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>k</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>R</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>G=textbf {Aut}(A),~G(k)/R=1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=application/x-tex>A</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is an Albert division algebra over <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=k> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=application/x-tex>k</mml:annotation> </mml:semantics> </mml:math> </inline-formula> as above and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper R> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding=application/x-tex>R</mml:annotation> </mml:semantics> </mml:math> </inline-formula> stands for <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper R> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding=application/x-tex>R</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-equivalence in the sense of Manin." @default.
• W2000592162 created "2016-06-24" @default.
• W2000592162 creator A5022017727 @default.
• W2000592162 date "2012-11-28" @default.
• W2000592162 modified "2023-10-16" @default.
• W2000592162 title "Automorphisms of Albert algebras and a conjecture of Tits and Weiss" @default.
• W2000592162 cites W1506692979 @default.
• W2000592162 cites W1564278681 @default.
• W2000592162 cites W1584561919 @default.
• W2000592162 cites W1644487517 @default.
• W2000592162 cites W1964827884 @default.
• W2000592162 cites W1966607921 @default.
• W2000592162 cites W1969177372 @default.
• W2000592162 cites W1983342471 @default.
• W2000592162 cites W2010415161 @default.
• W2000592162 cites W2022946056 @default.
• W2000592162 cites W2023968833 @default.
• W2000592162 cites W2034565751 @default.
• W2000592162 cites W2036357726 @default.
• W2000592162 cites W2046009902 @default.
• W2000592162 cites W2066114766 @default.
• W2000592162 cites W2091148878 @default.
• W2000592162 cites W2091384925 @default.
• W2000592162 cites W2144798024 @default.
• W2000592162 cites W2315213025 @default.
• W2000592162 cites W4210405807 @default.
• W2000592162 cites W4210837204 @default.
• W2000592162 cites W4231534425 @default.
• W2000592162 cites W4243894389 @default.
• W2000592162 cites W4253896101 @default.
• W2000592162 doi "https://doi.org/10.1090/s0002-9947-2012-05710-2" @default.
• W2000592162 hasPublicationYear "2012" @default.
• W2000592162 type Work @default.
• W2000592162 sameAs 2000592162 @default.
• W2000592162 citedByCount "11" @default.
• W2000592162 countsByYear W20005921622014 @default.
• W2000592162 countsByYear W20005921622016 @default.
• W2000592162 countsByYear W20005921622017 @default.
• W2000592162 countsByYear W20005921622019 @default.
• W2000592162 countsByYear W20005921622020 @default.
• W2000592162 countsByYear W20005921622021 @default.
• W2000592162 countsByYear W20005921622022 @default.
• W2000592162 crossrefType "journal-article" @default.
• W2000592162 hasAuthorship W2000592162A5022017727 @default.
• W2000592162 hasBestOaLocation W20005921621 @default.
• W2000592162 hasConcept C114614502 @default.
• W2000592162 hasConcept C118712358 @default.
• W2000592162 hasConcept C136119220 @default.
• W2000592162 hasConcept C138354692 @default.
• W2000592162 hasConcept C14394260 @default.
• W2000592162 hasConcept C169654258 @default.
• W2000592162 hasConcept C202444582 @default.
• W2000592162 hasConcept C2780990831 @default.
• W2000592162 hasConcept C33923547 @default.
• W2000592162 hasConcept C54732982 @default.
• W2000592162 hasConcept C74193536 @default.
• W2000592162 hasConcept C9652623 @default.
• W2000592162 hasConceptScore W2000592162C114614502 @default.
• W2000592162 hasConceptScore W2000592162C118712358 @default.
• W2000592162 hasConceptScore W2000592162C136119220 @default.
• W2000592162 hasConceptScore W2000592162C138354692 @default.
• W2000592162 hasConceptScore W2000592162C14394260 @default.
• W2000592162 hasConceptScore W2000592162C169654258 @default.
• W2000592162 hasConceptScore W2000592162C202444582 @default.
• W2000592162 hasConceptScore W2000592162C2780990831 @default.
• W2000592162 hasConceptScore W2000592162C33923547 @default.
• W2000592162 hasConceptScore W2000592162C54732982 @default.
• W2000592162 hasConceptScore W2000592162C74193536 @default.
• W2000592162 hasConceptScore W2000592162C9652623 @default.
• W2000592162 hasLocation W20005921621 @default.
• W2000592162 hasLocation W20005921622 @default.
• W2000592162 hasLocation W20005921623 @default.
• W2000592162 hasOpenAccess W2000592162 @default.
• W2000592162 hasPrimaryLocation W20005921621 @default.
• W2000592162 hasRelatedWork W1504623053 @default.
• W2000592162 hasRelatedWork W1506692979 @default.
• W2000592162 hasRelatedWork W1511683753 @default.
• W2000592162 hasRelatedWork W1529828874 @default.
• W2000592162 hasRelatedWork W1555621010 @default.
• W2000592162 hasRelatedWork W1584561919 @default.
• W2000592162 hasRelatedWork W1644487517 @default.
• W2000592162 hasRelatedWork W1966607921 @default.
• W2000592162 hasRelatedWork W1994421245 @default.
• W2000592162 hasRelatedWork W2010415161 @default.
• W2000592162 hasRelatedWork W2016752473 @default.
• W2000592162 hasRelatedWork W2037891561 @default.
• W2000592162 hasRelatedWork W2076233378 @default.
• W2000592162 hasRelatedWork W211457683 @default.
• W2000592162 hasRelatedWork W2144798024 @default.
• W2000592162 hasRelatedWork W2552053076 @default.
• W2000592162 hasRelatedWork W2774810288 @default.
• W2000592162 hasRelatedWork W2790437186 @default.
• W2000592162 hasRelatedWork W3011872810 @default.
• W2000592162 hasRelatedWork W3136172680 @default.
• W2000592162 isParatext "false" @default.
• W2000592162 isRetracted "false" @default.
• W2000592162 magId "2000592162" @default.
• W2000592162 workType "article" @default.