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Generators and relations for (generalised) Cartan type superalgebras. (arXiv:1812.03068v1 [math.RT])
来源于:arXiv
In Kac's classification of finite-dimensional Lie superalgebras, the
contragredient ones can be constructed from Dynkin diagrams similar to those of
the simple finite-dimensional Lie algebras, but with additional types of nodes.
For example, $A(n-1,0) = \mathfrak{sl}(1|n)$ can be constructed by adding a
"gray" node to the Dynkin diagram of $A_{n-1} = \mathfrak{sl}(n)$,
corresponding to an odd null root. The Cartan superalgebras constitute a
different class, where the simplest example is $W(n)$, the derivation algebra
of the Grassmann algebra on $n$ generators. Here we present a novel
construction of $W(n)$, from the same Dynkin diagram as $A(n-1,0)$, but with
additional generators and relations. 查看全文>>