Matches in SemOpenAlex for { <https://semopenalex.org/work/W2140604077> ?p ?o ?g. }
Showing items 1 to 89 of
89
with 100 items per page.
- W2140604077 abstract "Generalizing a theorem of Albert, Saltman showed that an Azumaya algebra $A$ over a ring represents a $2$-torsion class in the Brauer group if and only if there is an algebra $A'$ in the Brauer class of $A$ admitting an involution of the first kind. Knus, Parimala, and Srinivas later showed that one can choose $A'$ such that $mathrm{deg}, A'=2mathrm{deg}, A$. We show that $2mathrm{deg}, A$ is the lowest degree one can expect in general. Specifically, we construct an Azumaya algebra $A$ of degree $4$ and period $2$ such that the degree of any algebra $A'$ in the Brauer class of $A$ admitting an involution is divisible by $8$. Separately, we provide examples of split and non-split Azumaya algebras of degree $2$ admitting symplectic involutions, but no orthogonal involutions. These stand in contrast to the case of central simple algebras of even degree over fields, where the presence of a symplectic involution implies the existence of an orthogonal involution and vice versa." @default.
- W2140604077 created "2016-06-24" @default.
- W2140604077 creator A5021111412 @default.
- W2140604077 creator A5056368545 @default.
- W2140604077 creator A5065681499 @default.
- W2140604077 date "2015-10-21" @default.
- W2140604077 modified "2023-09-27" @default.
- W2140604077 title "Azumaya Algebras of Period 2 Without Involution" @default.
- W2140604077 cites W1496887040 @default.
- W2140604077 cites W1541776832 @default.
- W2140604077 cites W1644487517 @default.
- W2140604077 cites W2007396659 @default.
- W2140604077 cites W2015465448 @default.
- W2140604077 cites W2016117291 @default.
- W2140604077 cites W2043073725 @default.
- W2140604077 cites W2071852965 @default.
- W2140604077 cites W2076149810 @default.
- W2140604077 cites W2087293935 @default.
- W2140604077 cites W2087752299 @default.
- W2140604077 cites W2322831583 @default.
- W2140604077 cites W2328632474 @default.
- W2140604077 cites W3040586665 @default.
- W2140604077 cites W638338753 @default.
- W2140604077 cites W77377904 @default.
- W2140604077 hasPublicationYear "2015" @default.
- W2140604077 type Work @default.
- W2140604077 sameAs 2140604077 @default.
- W2140604077 citedByCount "0" @default.
- W2140604077 crossrefType "posted-content" @default.
- W2140604077 hasAuthorship W2140604077A5021111412 @default.
- W2140604077 hasAuthorship W2140604077A5056368545 @default.
- W2140604077 hasAuthorship W2140604077A5065681499 @default.
- W2140604077 hasConcept C136119220 @default.
- W2140604077 hasConcept C138354692 @default.
- W2140604077 hasConcept C141071460 @default.
- W2140604077 hasConcept C168619227 @default.
- W2140604077 hasConcept C17744445 @default.
- W2140604077 hasConcept C199539241 @default.
- W2140604077 hasConcept C202444582 @default.
- W2140604077 hasConcept C2781409172 @default.
- W2140604077 hasConcept C33923547 @default.
- W2140604077 hasConcept C48605111 @default.
- W2140604077 hasConcept C62196294 @default.
- W2140604077 hasConcept C67996461 @default.
- W2140604077 hasConcept C71924100 @default.
- W2140604077 hasConcept C77461463 @default.
- W2140604077 hasConcept C94625758 @default.
- W2140604077 hasConceptScore W2140604077C136119220 @default.
- W2140604077 hasConceptScore W2140604077C138354692 @default.
- W2140604077 hasConceptScore W2140604077C141071460 @default.
- W2140604077 hasConceptScore W2140604077C168619227 @default.
- W2140604077 hasConceptScore W2140604077C17744445 @default.
- W2140604077 hasConceptScore W2140604077C199539241 @default.
- W2140604077 hasConceptScore W2140604077C202444582 @default.
- W2140604077 hasConceptScore W2140604077C2781409172 @default.
- W2140604077 hasConceptScore W2140604077C33923547 @default.
- W2140604077 hasConceptScore W2140604077C48605111 @default.
- W2140604077 hasConceptScore W2140604077C62196294 @default.
- W2140604077 hasConceptScore W2140604077C67996461 @default.
- W2140604077 hasConceptScore W2140604077C71924100 @default.
- W2140604077 hasConceptScore W2140604077C77461463 @default.
- W2140604077 hasConceptScore W2140604077C94625758 @default.
- W2140604077 hasLocation W21406040771 @default.
- W2140604077 hasOpenAccess W2140604077 @default.
- W2140604077 hasPrimaryLocation W21406040771 @default.
- W2140604077 hasRelatedWork W2001618379 @default.
- W2140604077 hasRelatedWork W2007058509 @default.
- W2140604077 hasRelatedWork W2018106632 @default.
- W2140604077 hasRelatedWork W2041092216 @default.
- W2140604077 hasRelatedWork W2045558355 @default.
- W2140604077 hasRelatedWork W2066827872 @default.
- W2140604077 hasRelatedWork W2076019846 @default.
- W2140604077 hasRelatedWork W2116318750 @default.
- W2140604077 hasRelatedWork W2160547110 @default.
- W2140604077 hasRelatedWork W2326658916 @default.
- W2140604077 hasRelatedWork W2536499673 @default.
- W2140604077 hasRelatedWork W2741752921 @default.
- W2140604077 hasRelatedWork W2763447911 @default.
- W2140604077 hasRelatedWork W2764171736 @default.
- W2140604077 hasRelatedWork W2884760570 @default.
- W2140604077 hasRelatedWork W2949220029 @default.
- W2140604077 hasRelatedWork W2949769795 @default.
- W2140604077 hasRelatedWork W2953095050 @default.
- W2140604077 hasRelatedWork W2963929774 @default.
- W2140604077 hasRelatedWork W1756719161 @default.
- W2140604077 isParatext "false" @default.
- W2140604077 isRetracted "false" @default.
- W2140604077 magId "2140604077" @default.
- W2140604077 workType "article" @default.