Alphabeta MathHow statement and proof provenance work
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Bracket data for gl(1|1)
Definition
Let , with even and odd. Define a complex-bilinear bracket on this graded vector space by with ; all reversed even–odd brackets are determined by graded skew symmetry. Denote this bracketed graded vector space by the gl(1|1) bracket data. The next item proves that it is a Lie superalgebra; until then this definition is only the specified vector space and bracket table.
Depends on
Used by
- Finite-dimensional Lie supermodule categories need not be semisimple Counterexample
- Two-dimensional highest-weight module data for gl(1|1) Definition
- An odd abelian subalgebra has an exterior enveloping algebra Example
- The gl(1|1) bracket data define a Lie superalgebra Theorem
- The two-dimensional gl(1|1) action is well-defined Theorem
Dependency tree · two levels
3 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Sigiswald Barbier, A minimal representation for the orthosymplectic Lie-superalgebra, §§2.2 and 2.3.1 (standard reference, not scraped)
- Victor Kac, Classification of Supersymmetries, §2 (standard reference, not scraped)