Premium
Homology and cohomology operations in terms of differential operators
Author(s) -
Brunetti Maurizio,
Ciampella Adriana,
Lomonaco Luciano A.
Publication year - 2010
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdp097
Subject(s) - mathematics , steenrod algebra , differential operator , cohomology , homology (biology) , pure mathematics , algebra over a field , gene , biochemistry , chemistry
We consider some actions of the universal Steenrod algebra on the graded algebra of finite Laurent series L ( n ) = 2 [ x 1 ± 1 , … , x n ± 1]compatible with the familiar action of the ordinary Steenrod algebra on H * ((ℝℙ ∞ ) n , 2 ). The induced actions of the lambda algebra and the Dyer–Lashof algebra ℛ on L( n ) − = 2 [ x 1 − 1 , … , x n − 1]are also studied. It turns out that the negative generators of 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 ) − .