Sheared algebra maps and operation bialgebras for mod 2 homology and cohomology |
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Authors: | David J Pengelley Frank Williams |
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Institution: | Department of Mathematics, New Mexico State University, Las Cruces, New Mexico 88003 ; Department of Mathematics, New Mexico State University, Las Cruces, New Mexico 88003 |
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Abstract: | The mod 2 Steenrod algebra and Dyer-Lashof algebra have both striking similarities and differences arising from their common origins in ``lower-indexed' algebraic operations. These algebraic operations and their relations generate a bigraded bialgebra , whose module actions are equivalent to, but quite different from, those of and . The exact relationships emerge as ``sheared algebra bijections', which also illuminate the role of the cohomology of . As a bialgebra, has a particularly attractive and potentially useful structure, providing a bridge between those of and , and suggesting possible applications to the Miller spectral sequence and the structure of Dickson algebras. |
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Keywords: | Steenrod algebra Dyer-Lashof algebra bialgebras sheared algebra map Kudo-Araki-May algebra Nishida relations |
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