Symmetries of modules of differential operators on the supercircle $$S^{1|n} $$

Autor: I. Safi, J. Boujelben, K. Tounsi, Z. Saoudi
Rok vydání: 2021
Předmět:
Zdroj: Indian Journal of Pure and Applied Mathematics. 53:701-719
ISSN: 0975-7465
0019-5588
DOI: 10.1007/s13226-021-00164-y
Popis: Let $$\mathfrak {F}_{\lambda }^n$$ be the space of tensor densities of degree $$\lambda \in \mathbb {C}$$ on the supercircle $$S^{1|n}$$ . We consider the space $$\mathfrak {D}_{\lambda ,\mu }^{n,k}$$ of k-th order linear differential operators from $$\mathfrak {F}_{\lambda }^n$$ to $$\mathfrak {F}_{\mu }^n$$ as a module over the superalgebra $$\mathcal {K}(n)$$ of contact vector fields on $$S^{1|n}$$ and we compute the superalgebra of endomrphisms on $$\mathfrak {D}_{\lambda ,\mu }^{n,k}$$ commuting with the $$\mathfrak {aff}(n|1)$$ -action where $$\mathfrak {aff}(n|1)$$ is the affine subalgebra of $$\mathcal {K}(n)$$ . This result allows us to determine the superalgebra of endomrphisms on $$\mathfrak {D}_{\lambda ,\mu }^{n,k}$$ commuting with the $$\mathfrak {osp}(n|2)$$ -action for $$n\in \{1,2,3\}$$ where $$\mathfrak {osp}(n|2)$$ is the orthosymlectic superalgebras of $$S^{1|n}$$ .
Databáze: OpenAIRE
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