Homology of Lie algebra of supersymmetries and of super Poincare Lie algebra

A. Schwarz; M.V. Movshev; Renjun Xu

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Homology of Lie algebra of supersymmetries and of super Poincare Lie algebra

M.V. Movshev, A. Schwarz, Renjun Xu

High Energy Physics - Theory · Submitted 1 Jun 2011

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The authors' main claim We give complete answers for (non-extended) supersymmetry in all dimensions $\leq 11$.

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arXiv ID1106.0335 (version 3)

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CitationA. Schwarz, M.V. Movshev, Renjun Xu. "Homology of Lie algebra of supersymmetries and of super Poincare Lie algebra." arXiv:1106.0335 (2011). https://pith.science/paper/JNZWUUBM

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We study the homology and cohomology groups of super Lie algebra of supersymmetries and of super Poincare Lie algebra in various dimensions. We give complete answers for (non-extended) supersymmetry in all dimensions $\leq 11$. For dimensions $D=10,11$ we describe also the cohomology of reduction of supersymmetry Lie algebra to lower dimensions. Our methods can be applied to extended supersymmetry algebra.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study the homology and cohomology groups of super Lie algebra of supersymmetries and of super Poincare Lie algebra in various dimensions.	contribution 0.98	0.92	0.09	asserted 0.92
s1	We give complete answers for (non-extended) supersymmetry in all dimensions $\leq 11$.	result 0.83	0.95	0.46	asserted 1.00
s2	For dimensions $D=10,11$ we describe also the cohomology of reduction of supersymmetry Lie algebra to lower dimensions.	result 0.54	0.93	0.11	asserted 1.00
s3	Our methods can be applied to extended supersymmetry algebra.	future work 0.69	0.42	0.06	hedged possibility 0.54

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Original abstract

We study the homology and cohomology groups of super Lie algebra of supersymmetries and of super Poincare Lie algebra in various dimensions. We give complete answers for (non-extended) supersymmetry in all dimensions $\leq 11$. For dimensions $D=10,11$ we describe also the cohomology of reduction of supersymmetry Lie algebra to lower dimensions. Our methods can be applied to extended supersymmetry algebra.

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8 arXiv papers cite this in 21 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 14 sentences without a confident label

Builds on it 2 papers

[ref] , and extend them to all numbers of supersymmetries and all signatures.

Supersymmetry algebra cohomology IV: Primitive elements in all dimensions from D=4 to D=11 · Introduction · 0.92
This analysis was extended by Movshev, Schwarz, and Xu to the super-Poincaré algebra in [ref] .

Superspace de Rham Complex and Relative Cohomology · The Chevalley-Eilenberg Complex · 0.84

Uses its method or tool 1 paper

One can calculate it using the methods of [ref] .

Integral invariants in flat superspace · $N=2$ superspace in $10D$ · 1.00

Uses its data or values 1 paper

To find the part of $A^p$ corresponding to the group $ℋ^p,q_s$ we should use (<ref>) and the $t$-degrees of elements of $μ^p_m$ (this information can be found in [ref] ).

Integral invariants in flat superspace · Groups $H^p,q_t$ and $H^p,q_s$ : general results · 0.90

Compares with it 1 paper

[ref] for $=8$ because there, using the notation of the present paper, cocycles with $113$, $11, a3$, $11, ab3$ in place of $113$, $11, a3$, $11, ab3$ are presented.

Supersymmetry algebra cohomology IV: Primitive elements in all dimensions from D=4 to D=11 · Primitive elements in D=8 · 0.90

Cites it as background 1 paper

Some of these multiplets were studied for various super Poincaré algebras in [ref] ; see also [ref] .

The Derived Pure Spinor Formalism as an Equivalence of Categories · Multiplets from Lie algebra cohomology · 0.80

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In particular, combining them with considerations of [ref] one can analyze the structure of supersymmetric invariants in situations that were not considered in [ref] .

The cohomology of superspace, pure spinors and invariant integrals · Introduction · 0.94

Uses the method or tool of 1 paper

We prove that our formulas give cocycles using Gamma [ref] .

GAMMA: A Mathematica package for performing gamma-matrix algebra and Fierz transformations in arbitrary dimensions · Computer calculations · 1.00

Cites as background 2 papers

In low dimensions it was studied in [ref] .

Supersymmetry algebra cohomology I: Definition and general structure · Introduction · 0.82
The cohomology of supersymmetry Lie algebras appeared in the analysis of supersymmetric invariants in [ref] (it was denoted there by the symbol $H^p,q_t$).

The cohomology of superspace, pure spinors and invariant integrals · Introduction · 0.92

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