FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2130187198> ?p ?o ?g. }

• W2130187198 endingPage "1054" @default.
• W2130187198 startingPage "1043" @default.
• W2130187198 abstract "The purpose of this paper is to classify invariant hypercomplex structures on a <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=4> <mml:semantics> <mml:mn>4</mml:mn> <mml:annotation encoding=application/x-tex>4</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-dimensional real Lie group <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=application/x-tex>G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. It is shown that the <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=4> <mml:semantics> <mml:mn>4</mml:mn> <mml:annotation encoding=application/x-tex>4</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-dimensional simply connected Lie groups which admit invariant hypercomplex structures are the additive group <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=double-struck upper H> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>H</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathbb H</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of the quaternions, the multiplicative group <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=double-struck upper H Superscript asterisk> <mml:semantics> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>H</mml:mi> </mml:mrow> </mml:mrow> <mml:mo>∗<!-- ∗ --></mml:mo> </mml:msup> <mml:annotation encoding=application/x-tex>{mathbb H}^*</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of nonzero quaternions, the solvable Lie groups acting simply transitively on the real and complex hyperbolic spaces, <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=double-struck upper R upper H Superscript 4> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>R</mml:mi> </mml:mrow> </mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>4</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>{mathbb R}H^4</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=double-struck upper C upper H squared> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>C</mml:mi> </mml:mrow> </mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>{mathbb C}H^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, respectively, and the semidirect product <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=double-struck upper C right-normal-factor-semidirect-product double-struck upper C> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>C</mml:mi> </mml:mrow> </mml:mrow> <mml:mo>⋊<!-- ⋊ --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>C</mml:mi> </mml:mrow> </mml:mrow> </mml:mrow> <mml:annotation encoding=application/x-tex>{mathbb C}rtimes {mathbb C}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We show that the spaces <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=double-struck upper C upper H squared> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>C</mml:mi> </mml:mrow> </mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>{mathbb C}H^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=double-struck upper C right-normal-factor-semidirect-product double-struck upper C> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>C</mml:mi> </mml:mrow> </mml:mrow> <mml:mo>⋊<!-- ⋊ --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>C</mml:mi> </mml:mrow> </mml:mrow> <mml:mspace width=thinmathspace /> </mml:mrow> <mml:annotation encoding=application/x-tex>{mathbb C}rtimes {mathbb C},</mml:annotation> </mml:semantics> </mml:math> </inline-formula> possess an <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=double-struck upper R upper P squared> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>R</mml:mi> </mml:mrow> </mml:mrow> <mml:msup> <mml:mi>P</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>{mathbb R}P^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of (inequivalent) invariant hypercomplex structures while the remaining groups have only one, up to equivalence. Finally, the corresponding hyperhermitian <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=4> <mml:semantics> <mml:mn>4</mml:mn> <mml:annotation encoding=application/x-tex>4</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-manifolds are determined." @default.
• W2130187198 created "2016-06-24" @default.
• W2130187198 creator A5066456240 @default.
• W2130187198 date "1997-01-01" @default.
• W2130187198 modified "2023-10-14" @default.
• W2130187198 title "Hypercomplex structures on four-dimensional Lie groups" @default.
• W2130187198 cites W149113236 @default.
• W2130187198 cites W1605212418 @default.
• W2130187198 cites W1983242372 @default.
• W2130187198 cites W2000990964 @default.
• W2130187198 cites W2027428352 @default.
• W2130187198 cites W2043367246 @default.
• W2130187198 cites W2597170910 @default.
• W2130187198 cites W4239445650 @default.
• W2130187198 doi "https://doi.org/10.1090/s0002-9939-97-03611-3" @default.
• W2130187198 hasPublicationYear "1997" @default.
• W2130187198 type Work @default.
• W2130187198 sameAs 2130187198 @default.
• W2130187198 citedByCount "51" @default.
• W2130187198 countsByYear W21301871982013 @default.
• W2130187198 countsByYear W21301871982016 @default.
• W2130187198 countsByYear W21301871982017 @default.
• W2130187198 countsByYear W21301871982018 @default.
• W2130187198 countsByYear W21301871982019 @default.
• W2130187198 countsByYear W21301871982020 @default.
• W2130187198 countsByYear W21301871982021 @default.
• W2130187198 countsByYear W21301871982022 @default.
• W2130187198 countsByYear W21301871982023 @default.
• W2130187198 crossrefType "journal-article" @default.
• W2130187198 hasAuthorship W2130187198A5066456240 @default.
• W2130187198 hasBestOaLocation W21301871981 @default.
• W2130187198 hasConcept C11413529 @default.
• W2130187198 hasConcept C154945302 @default.
• W2130187198 hasConcept C200127275 @default.
• W2130187198 hasConcept C203249530 @default.
• W2130187198 hasConcept C2524010 @default.
• W2130187198 hasConcept C2776321320 @default.
• W2130187198 hasConcept C33923547 @default.
• W2130187198 hasConcept C41008148 @default.
• W2130187198 hasConceptScore W2130187198C11413529 @default.
• W2130187198 hasConceptScore W2130187198C154945302 @default.
• W2130187198 hasConceptScore W2130187198C200127275 @default.
• W2130187198 hasConceptScore W2130187198C203249530 @default.
• W2130187198 hasConceptScore W2130187198C2524010 @default.
• W2130187198 hasConceptScore W2130187198C2776321320 @default.
• W2130187198 hasConceptScore W2130187198C33923547 @default.
• W2130187198 hasConceptScore W2130187198C41008148 @default.
• W2130187198 hasIssue "4" @default.
• W2130187198 hasLocation W21301871981 @default.
• W2130187198 hasOpenAccess W2130187198 @default.
• W2130187198 hasPrimaryLocation W21301871981 @default.
• W2130187198 hasRelatedWork W2026218351 @default.
• W2130187198 hasRelatedWork W2044767466 @default.
• W2130187198 hasRelatedWork W2146426283 @default.
• W2130187198 hasRelatedWork W2800395957 @default.
• W2130187198 hasRelatedWork W2916518000 @default.
• W2130187198 hasRelatedWork W3082235301 @default.
• W2130187198 hasRelatedWork W3125691543 @default.
• W2130187198 hasRelatedWork W3185621658 @default.
• W2130187198 hasRelatedWork W4300216686 @default.
• W2130187198 hasRelatedWork W1578004053 @default.
• W2130187198 hasVolume "125" @default.
• W2130187198 isParatext "false" @default.
• W2130187198 isRetracted "false" @default.
• W2130187198 magId "2130187198" @default.
• W2130187198 workType "article" @default.