Mohamed Nayam | University of Bahrain (original) (raw)

Papers by Mohamed Nayam

Research paper thumbnail of Homology rings of homotopy associative H-spaces

Topology and Its Applications, 2008

Let X be a homotopy associative mod p H-space for p an odd prime. The homology H * (X; F p ) is a... more Let X be a homotopy associative mod p H-space for p an odd prime. The homology H * (X; F p ) is an associative ring, but not necessarily commutative. We study conditions when [x, y] = 0 for x, y elements of H * (X; F p ). Under certain conditions [x, y] = 0 imply ad l (x, y) = 0 for l = p − 2 or p − 1. These methods can be used to prove results about homology commutators that were previously obtained using the adjoint action [H. Hamanaka, S. Hara, A. Kono, Adjoint action of Lie groups on the loop spaces and cohomology of exceptional Lie groups, Transform. Group Theory (1996) 44-50, Korea Adv. Inst. Sci. Tech.; A. Kono, K. Kozima, The adjoint action of a Lie group on the space of loops, J. Math. Soc. Japan 45 (3) (1993) 495-509; A. Kono, J. Lin, O. Nishimura, Characterization of the mod 3 cohomology of E 7 , Proc. Amer. Math. Soc. 131 (10) (2003) 3289-3295]. We also generalize results of Kane [R. Kane, Torsion in homotopy associative H-spaces, Illinois J. Math. 20 (1976) 476-485] to nonfinite mod p homotopy associative H-spaces.

Research paper thumbnail of Homology rings of homotopy associative H-spaces

Topology and Its Applications, 2008

Let X be a homotopy associative mod p H-space for p an odd prime. The homology H * (X; F p ) is a... more Let X be a homotopy associative mod p H-space for p an odd prime. The homology H * (X; F p ) is an associative ring, but not necessarily commutative. We study conditions when [x, y] = 0 for x, y elements of H * (X; F p ). Under certain conditions [x, y] = 0 imply ad l (x, y) = 0 for l = p − 2 or p − 1. These methods can be used to prove results about homology commutators that were previously obtained using the adjoint action [H. Hamanaka, S. Hara, A. Kono, Adjoint action of Lie groups on the loop spaces and cohomology of exceptional Lie groups, Transform. Group Theory (1996) 44-50, Korea Adv. Inst. Sci. Tech.; A. Kono, K. Kozima, The adjoint action of a Lie group on the space of loops, J. Math. Soc. Japan 45 (3) (1993) 495-509; A. Kono, J. Lin, O. Nishimura, Characterization of the mod 3 cohomology of E 7 , Proc. Amer. Math. Soc. 131 (10) (2003) 3289-3295]. We also generalize results of Kane [R. Kane, Torsion in homotopy associative H-spaces, Illinois J. Math. 20 (1976) 476-485] to nonfinite mod p homotopy associative H-spaces.