数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (4): 1193-1211.doi: 10.1016/S0252-9602(14)60079-5

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ON INVERSES AND ALGEBRAIC LOOPS OF CO-H-SPACES

Dae-Woong LEE   

  1. Department of Mathematics, and Institute of Pure and Applied Mathematics, Chonbuk National University, 567 Baekje-daero, Deokjin-gu, Jeonju-si, Jeollabuk-do 561-756, Republic of Korea
  • 收稿日期:2013-01-14 修回日期:2013-06-20 出版日期:2014-07-20 发布日期:2014-07-20
  • 基金资助:

    This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0022035).

ON INVERSES AND ALGEBRAIC LOOPS OF CO-H-SPACES

Dae-Woong LEE   

  1. Department of Mathematics, and Institute of Pure and Applied Mathematics, Chonbuk National University, 567 Baekje-daero, Deokjin-gu, Jeonju-si, Jeollabuk-do 561-756, Republic of Korea
  • Received:2013-01-14 Revised:2013-06-20 Online:2014-07-20 Published:2014-07-20
  • Supported by:

    This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0022035).

摘要:

In this paper we study the properties of homotopy inverses of comultiplications and algebraic loops of co-H-spaces based on a wedge of spheres. We also investigate a method to construct new comultiplications out of old ones by using a group action. We are primar-ily interested in the algebraic loops which have inversive, power-associative and Moufang
properties for some comultiplications.

关键词: inverses, co-H-spaces, comultiplications, basic (Whitehead) product, Hopf-Hilton invariants, algebraic loops, inversivity, power-associativity, Moufang property

Abstract:

In this paper we study the properties of homotopy inverses of comultiplications and algebraic loops of co-H-spaces based on a wedge of spheres. We also investigate a method to construct new comultiplications out of old ones by using a group action. We are primar-ily interested in the algebraic loops which have inversive, power-associative and Moufang
properties for some comultiplications.

Key words: inverses, co-H-spaces, comultiplications, basic (Whitehead) product, Hopf-Hilton invariants, algebraic loops, inversivity, power-associativity, Moufang property

中图分类号: 

  • 55P45