We consider some actions of the universal Steenrod algebra Q on the graded algebra of finite Laurent series L(n) in n indeterminates compatible with the familiar action of the ordinary Steenrod algebra A on the cohomology of the infinite dimensional projective space. The induced actions of the lambda algebra Λ and the Dyer–Lashof algebra R on a certain subalgebra L(n)͞ of L(n) are also studied. It turns out that the Negatively indexed generators of Q do not act as differential operators on L(n), if the Cartan formula holds. We also prove that neither Λ nor R are differential operator algebras when they act non-trivially on L(n)͞ .

Homology and cohomology operations in terms of differential operators / Brunetti, Maurizio; Ciampella, Adriana; Lomonaco, LUCIANO AMITO. - In: BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6093. - STAMPA. - (2010), pp. 53-63. [10.1112/blms/bdp097]

Homology and cohomology operations in terms of differential operators

BRUNETTI, MAURIZIO
;
CIAMPELLA, ADRIANA;LOMONACO, LUCIANO AMITO
2010

Abstract

We consider some actions of the universal Steenrod algebra Q on the graded algebra of finite Laurent series L(n) in n indeterminates compatible with the familiar action of the ordinary Steenrod algebra A on the cohomology of the infinite dimensional projective space. The induced actions of the lambda algebra Λ and the Dyer–Lashof algebra R on a certain subalgebra L(n)͞ of L(n) are also studied. It turns out that the Negatively indexed generators of Q do not act as differential operators on L(n), if the Cartan formula holds. We also prove that neither Λ nor R are differential operator algebras when they act non-trivially on L(n)͞ .
2010
Homology and cohomology operations in terms of differential operators / Brunetti, Maurizio; Ciampella, Adriana; Lomonaco, LUCIANO AMITO. - In: BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6093. - STAMPA. - (2010), pp. 53-63. [10.1112/blms/bdp097]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/360578
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