For a simple complex Lie algebra g we study the space of g-invariants in the tensor product of the exterior algebra of g^* with g^*, which describes the isotypic component of type g in the exterior algebra, as a module over the algebra of invariants. As main result we prove that A is a free module, of rank twice the rank of g, over the exterior algebra generated by all primitive invariants with the exception of the one of highest degree.

The adjoint representation inside the exterior algebra of a simple Lie algebra / De Concini, Corrado; Papi, Paolo; Procesi, Claudio. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - STAMPA. - 280:(2015), pp. 21-46. [10.1016/j.aim.2015.04.011]

The adjoint representation inside the exterior algebra of a simple Lie algebra

DE CONCINI, Corrado;PAPI, Paolo;PROCESI, Claudio
2015

Abstract

For a simple complex Lie algebra g we study the space of g-invariants in the tensor product of the exterior algebra of g^* with g^*, which describes the isotypic component of type g in the exterior algebra, as a module over the algebra of invariants. As main result we prove that A is a free module, of rank twice the rank of g, over the exterior algebra generated by all primitive invariants with the exception of the one of highest degree.
2015
Exterior algebra; invariants; transgression
01 Pubblicazione su rivista::01a Articolo in rivista
The adjoint representation inside the exterior algebra of a simple Lie algebra / De Concini, Corrado; Papi, Paolo; Procesi, Claudio. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - STAMPA. - 280:(2015), pp. 21-46. [10.1016/j.aim.2015.04.011]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/782197
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