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تسجيل مستخدم جديدHomology of Lie algebra of supersymmetries and of super Poincare Lie algebra
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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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We study the homology and cohomology groups of super Lie algebra of supersymmetries and of super Poincare algebra. We discuss in detail the calculation in dimensions D=10 and D=6. Our methods can be applied to extended supersymmetry algebra and to other dimensions.
We define a supersymmetric quantum mechanics of fermions that take values in a simple Lie algebra. We summarize what is known about the spectrum and eigenspaces of the Laplacian which corresponds to the Koszul differential d. Firstly, we concentrate
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-matrices of super-Abelian and super-Jordanian type. Corresponding twists describing quantum deformations are obtained in an explicit form. These twists are the super-extensions of twists obtained in the paper arXiv:0712.3962.
Let $L$ be a Lie algebra of Block type over $C$ with basis ${L_{alpha,i},|,alpha,iinZ}$ and brackets $[L_{alpha,i},L_{beta,j}]=(beta(i+1)-alpha(j+1))L_{alpha+beta,i+j}$. In this paper, we shall construct a formal distribution Lie algebra of $L$. Then
we decide its conformal algebra $B$ with $C[partial]$-basis ${L_alpha(w),|,alphainZ}$ and $lambda$-brackets $[L_alpha(w)_lambda L_beta(w)]=(alphapartial+(alpha+beta)lambda)L_{alpha+beta}(w)$. Finally, we give a classification of free intermediate series $B$-modules.
From a commutative associative algebra $A$, the infinite dimensional unital 3-Lie Poisson algebra~$mathfrak{L}$~is constructed, which is also a canonical Nambu 3-Lie algebra, and the structure of $mathfrak{L}$ is discussed. It is proved that: (1) the
re is a minimal set of generators $S$ consisting of six vectors; (2) the quotient algebra $mathfrak{L}/mathbb{F}L_{0, 0}^0$ is a simple 3-Lie Poisson algebra; (3) four important infinite dimensional 3-Lie algebras: 3-Virasoro-Witt algebra $mathcal{W}_3$, $A_omega^delta$, $A_{omega}$ and the 3-$W_{infty}$ algebra can be embedded in $mathfrak{L}$.
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