Displaying similar documents to “Space of Second Order Linear Differential Operators As a Module Over the Lie Algebra of Vector Fields”

On representations of restricted Lie superalgebras

Yu-Feng Yao (2014)

Czechoslovak Mathematical Journal

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Simple modules for restricted Lie superalgebras are studied. The indecomposability of baby Kac modules and baby Verma modules is proved in some situation. In particular, for the classical Lie superalgebra of type A ( n | 0 ) , the baby Verma modules Z χ ( λ ) are proved to be simple for any regular nilpotent p -character χ and typical weight λ . Moreover, we obtain the dimension formulas for projective covers of simple modules with p -characters of standard Levi form.

On the ghost centre of Lie superalgebras

Maria Gorelik (2000)

Annales de l'institut Fourier

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We study the invariants of the universal enveloping algebra of a Lie superalgebra with respect to a certain “twisted” adjoint action.

Dual vector fields ii: calculating the Jacobian

Philip Feinsilver, René Schott (2006)

Banach Center Publications

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Given a Lie algebra with a chosen basis, the change of coordinates relating coordinates of the first and second kinds near the identity of the corresponding local group yields some remarkable vector fields and dual vector fields. One family of vector fields is dual to a representation of the Lie algebra acting on a Fock-type space. To this representation an abelian family of dual vector fields is associated. The exponential of these commuting operators acting on an appropriate vacuum...

Hom-Lie superalgebra structures on exceptional simple Lie superalgebras of vector fields

Liping Sun, Wende Liu (2017)

Open Mathematics

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According to the classification by Kac, there are eight Cartan series and five exceptional Lie superalgebras in infinite-dimensional simple linearly compact Lie superalgebras of vector fields. In this paper, the Hom-Lie superalgebra structures on the five exceptional Lie superalgebras of vector fields are studied. By making use of the ℤ-grading structures and the transitivity, we prove that there is only the trivial Hom-Lie superalgebra structures on exceptional simple Lie superalgebras....