Archives

Transposition Algebras
by J. I. Hall  

Vol. 14 No. 2 (2019) P.155~P.187
DOI:
  10.21915/BIMAS.2019203

ABSTRACT

The symbiotic relationship between groups and algebras goes back at least to Sophus Lie, who introduced Lie algebras to support the study of Lie groups. Later the classification of finite dimensional, complex, semisimple Lie algebras was in turn reduced (primarily by Weyl) to the classification of finite groups generated by Euclidean reflections. The topics discussed here had a similar start. Algebras were introduced to aid in the construction of finite simple groups, particularly those that are sporadic. These algebras then found a broader context, and there groups were reintroduced to aid in construction and classification.


KEYWORDS
sporadic simple group, 3-transposition, Lie algebra, axial algebra

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: Primary: 20D05. Secondary: 17A99, 17B69

MILESTONES

Received: 2017-06-20
Revised : 2018-01-24
Accepted: 2018-04-10


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