Homology rings of homotopy associative H-spaces |
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Authors: | James P Lin |
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Institution: | University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0112, United States |
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Abstract: | Let X be a homotopy associative mod p H-space for p an odd prime. The homology H*(X;Fp) is an associative ring, but not necessarily commutative. We study conditions when for elements of H*(X;Fp). Under certain conditions imply 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 E7, 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. |
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Keywords: | 57T25 55R35 55S05 55S10 57T05 57T10 16W30 17B55 |
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