Lie superalgebra (Q2169): Difference between revisions

@@ Property / named after @@
+Sophus Lie
@@ Property / named after: Sophus Lie / rank @@
+Normal rank
@@ Property / Freebase ID @@
+/m/01rghv
@@ Property / Freebase ID: /m/01rghv / rank @@
+Normal rank
@@ Property / Freebase ID: /m/01rghv / reference @@
+stated in: Freebase Data Dumps
publication date: 28 October 2013Timestamp +2013-10-28T00:00:00Z
Timezone +00:00
Calendar Gregorian
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-Timestamp
++2013-10-28T00:00:00Z
-Timezone
++00:00
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+Gregorian
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@@ Property / Quora topic ID @@
+Lie-Superalgebra
@@ Property / Quora topic ID: Lie-Superalgebra / rank @@
+Normal rank
@@ Property / Quora topic ID: Lie-Superalgebra / reference @@
+stated in: Quora
@@ Property / subclass of @@
+super vector space
@@ Property / subclass of: super vector space / rank @@
+Normal rank
@@ Property / subclass of @@
+algebra over a field
@@ Property / subclass of: algebra over a field / rank @@
+Normal rank
@@ Property / FAST ID @@
@@ Property / FAST ID: 998136 / rank @@
+Normal rank
@@ Property / FAST ID: 998136 / reference @@
+stated in: Faceted Application of Subject Terminology
retrieved: 30 March 2018Timestamp +2018-03-30T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
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-Timestamp
++2018-03-30T00:00:00Z
-Timezone
++00:00
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+Gregorian
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@@ Property / Library of Congress authority ID @@
+sh94002764
@@ Property / Library of Congress authority ID: sh94002764 / rank @@
+Normal rank
@@ Property / Library of Congress authority ID: sh94002764 / reference @@
+stated in: Faceted Application of Subject Terminology
FAST ID: 998136
retrieved: 30 March 2018Timestamp +2018-03-30T00:00:00Z
Timezone +00:00
Calendar Gregorian
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-Timestamp
++2018-03-30T00:00:00Z
-Timezone
++00:00
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+Gregorian
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@@ Property / Bibliothèque nationale de France ID @@
+13191745r
@@ Property / Bibliothèque nationale de France ID: 13191745r / rank @@
+Normal rank
@@ Property / Bibliothèque nationale de France ID: 13191745r / reference @@
+stated in: Faceted Application of Subject Terminology
FAST ID: 998136
retrieved: 30 March 2018Timestamp +2018-03-30T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
Before 0
After 0
-Timestamp
++2018-03-30T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+day
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@@ Property / GND ID @@
+4304027-5
@@ Property / GND ID: 4304027-5 / rank @@
+Normal rank
@@ Property / GND ID: 4304027-5 / reference @@
+stated in: Integrated Authority File
retrieved: 30 March 2018Timestamp +2018-03-30T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
Before 0
After 0
-Timestamp
++2018-03-30T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
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+day
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@@ Property / IdRef ID @@
+03547128X
@@ Property / IdRef ID: 03547128X / rank @@
+Normal rank
@@ Property / IdRef ID: 03547128X / reference @@
+stated in: SUDOC
retrieved: 30 March 2018Timestamp +2018-03-30T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
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-Timestamp
++2018-03-30T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+day
 Before
 After
@@ Property / Microsoft Academic ID @@
+78804095
@@ Property / Microsoft Academic ID: 78804095 / rank @@
+Normal rank
@@ Property / OpenAlex ID @@
+C78804095
@@ Property / OpenAlex ID: C78804095 / rank @@
+Normal rank
@@ Property / OpenAlex ID: C78804095 / reference @@
+stated in: OpenAlex
retrieved: 26 January 2022Timestamp +2022-01-26T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
Before 0
After 0
reference URL: https://docs.openalex.org/download-snapshot/snapshot-data-format
-Timestamp
++2022-01-26T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+day
 Before
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@@ Property / National Library of Israel J9U ID @@
+987007534770405171
@@ Property / National Library of Israel J9U ID: 987007534770405171 / rank @@
+Normal rank
@@ Property / National Library of Israel J9U ID: 987007534770405171 / reference @@
+stated in: National Library of Israel Names and Subjects Authority File
@@ Property / ScienceDirect topic ID @@
+mathematics/lie-superalgebra
@@ Property / ScienceDirect topic ID: mathematics/lie-superalgebra / rank @@
+Normal rank
@@ Property / defining formula @@
+ ${\begin{aligned}{\mathfrak {g}}&={\mathfrak {g}}_{0}\oplus {\mathfrak {g}}_{1}\\{}[{\mathfrak {g}}_{i},{\mathfrak {g}}_{j}]&\subset {\mathfrak {g}}_{(i+j){\bmod {2}}}\\0&=[x,y]+(-1)^{|x||y|}[y,x]\\0&=(-1)^{|x||z|}[x,[y,z]]+(-1)^{|y||x|}[y,[z,x]]+(-1)^{|z||y|}[z,[x,y]]\\0&=[x,x]\qquad (x\in {\mathfrak {g}}_{0})\\0&=[x,[x,x]]\qquad (x\in {\mathfrak {g}}_{1})\end{aligned}}$ 
\begin{aligned}\mathfrak g&=\mathfrak g_0\oplus\mathfrak g_1\\{}[\mathfrak g_i,\mathfrak g_j]&\subset\mathfrak g_{(i+j)\bmod2}\\0&=[x,y]+(-1)^{|x||y|}[y,x]\\0&=(-1)^{|x||z|}[x,[y,z]]+(-1)^{|y||x|}[y,[z,x]]+(-1)^{|z||y|}[z,[x,y]]\\0&=[x,x]\qquad(x\in\mathfrak g_0)\\0&=[x,[x,x]]\qquad(x\in\mathfrak g_1)\end{aligned}
+Normal rank
@@ Property / in defining formula @@
+ ${\mathfrak {g}}$ 
\mathfrak g
@@ Property / in defining formula: ${\mathfrak {g}}$ / rank @@
+Normal rank
@@ Property / in defining formula: ${\mathfrak {g}}$ / qualifier @@
+symbol represents: Lie superalgebra
@@ Property / in defining formula @@
+ $[,]$ 
[,]
@@ Property / in defining formula: $[,]$ / rank @@
+Normal rank
@@ Property / in defining formula: $[,]$ / qualifier @@
+symbol represents: Lie bracket
@@ Property / in defining formula @@
+ ${\mathfrak {g}}_{0}$ 
\mathfrak g_0
@@ Property / in defining formula: ${\mathfrak {g}}_{0}$ / rank @@
+Normal rank
@@ Property / in defining formula: ${\mathfrak {g}}_{0}$ / qualifier @@
+symbol represents: Lie algebra
@@ Property / in defining formula @@
+ ${\mathfrak {g}}_{1}$ 
\mathfrak g_1
@@ Property / in defining formula: ${\mathfrak {g}}_{1}$ / rank @@
+Normal rank
@@ Property / in defining formula: ${\mathfrak {g}}_{1}$ / qualifier @@
+symbol represents: Lie algebra representation
@@ Property / nLab ID @@
+super Lie algebra
@@ Property / nLab ID: super Lie algebra / rank @@
+Normal rank
@@ Property / PlanetMath ID @@
+LieSuperalgebra
@@ Property / PlanetMath ID: LieSuperalgebra / rank @@
+Normal rank