On the axioms of Leibniz algebroids associated to Nambu-Poisson manifolds
Let $E \rightarrow M$ be a smooth vector bundle with a bilinear product on $\Gamma(E)$ satisfying the Jacobi identity. Assuming only the existence of an anchor map $\mathfrak{a}$ we show that $\mathfrak{a}([X,Y]) = [\mathfrak{a}X,\mathfrak{a}Y]_c$. This gives the redundancy of the homomorphism condi...
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| creator | Rau, S. Srinivas Shreecharan, T |
| description | Let $E \rightarrow M$ be a smooth vector bundle with a bilinear product on
$\Gamma(E)$ satisfying the Jacobi identity. Assuming only the existence of an
anchor map $\mathfrak{a}$ we show that $\mathfrak{a}([X,Y]) =
[\mathfrak{a}X,\mathfrak{a}Y]_c$. This gives the redundancy of the homomorphism
condition in the definition of Leibniz algebroid; in particular if it arises
from a Nambu-Poisson manifold. |
| doi_str_mv | 10.48550/arxiv.1510.07544 |
| format | Article |
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$\Gamma(E)$ satisfying the Jacobi identity. Assuming only the existence of an
anchor map $\mathfrak{a}$ we show that $\mathfrak{a}([X,Y]) =
[\mathfrak{a}X,\mathfrak{a}Y]_c$. This gives the redundancy of the homomorphism
condition in the definition of Leibniz algebroid; in particular if it arises
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$\Gamma(E)$ satisfying the Jacobi identity. Assuming only the existence of an
anchor map $\mathfrak{a}$ we show that $\mathfrak{a}([X,Y]) =
[\mathfrak{a}X,\mathfrak{a}Y]_c$. This gives the redundancy of the homomorphism
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$\Gamma(E)$ satisfying the Jacobi identity. Assuming only the existence of an
anchor map $\mathfrak{a}$ we show that $\mathfrak{a}([X,Y]) =
[\mathfrak{a}X,\mathfrak{a}Y]_c$. This gives the redundancy of the homomorphism
condition in the definition of Leibniz algebroid; in particular if it arises
from a Nambu-Poisson manifold.</abstract><doi>10.48550/arxiv.1510.07544</doi><oa>free_for_read</oa></addata></record> |
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| title | On the axioms of Leibniz algebroids associated to Nambu-Poisson manifolds |
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