Cohomology of finite monogenic self-distributive structures
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- 作者：Victoria Lebed lebed.victoria@gmail.com" class="auth_mail" title="E-mail the corresponding author Victoria.Lebed@univ-nantes.fr" class="auth_mail" title="E-mail the corresponding author
- 关键词：20N02 ; 55N35 ; 57M27
- 刊名：Journal of Pure and Applied Algebra
- 出版年：2016
- 出版时间：February 2016
- 年：2016
- 卷：220
- 期：2
- 页码：711-734
- 全文大小：512 K
文摘
A shelf is a set with a binary operation 鈻?satisfying a鈻?b鈻筩)=(a鈻筨)鈻?a鈻筩). Racks are shelves with invertible translations b鈫鈻筨; many of their aspects, including cohomological, are better understood than those of general shelves. Finite monogenic shelves (FMS), of which Laver tables and cyclic racks are the most famous examples, form a remarkably rich family of structures and play an important role in set theory. We compute the cohomology of FMS with arbitrary coefficients. On the way we develop general tools for studying the cohomology of shelves. Moreover, inside any finite shelf we identify a sub-rack which inherits its major characteristics, including the cohomology. For FMS, these sub-racks are all cyclic.