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The Monster algebra: Some new formulae. (English) Zbl 0847.11023
Dong, Chongying (ed.) et al., Moonshine, the Monster, and related topics. Joint summer research conference on moonshine, the Monster, and related topics, June 18-23, 1994, Mount Holyoke College, South Hadley, MA, USA. Providence, RI: American Mathematical Society. Contemp. Math. 193, 297-306 (1996).
The Monster is a 6-transposition Fischer group: it is generated by a class, 2A, of Fischer involutions (centralized by 2. Baby) such that any product of two has period $$\leq 6$$ and lies in one of 9 Monster classes. The classes and periods are in 1-1 correspondence with the coefficients of the highest root in the affine $$E_8$$ Lie algebra. This involution algebra is in the ATLAS [J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, Atlas of finite groups (Oxford 1985; Zbl 0568.20001)] and is studied in detail and counter-conjectures are made on relations with the Monster and moonshine.
For the entire collection see [Zbl 0831.00016].
Reviewer: J.McKay (Montreal)

##### MSC:
 11F22 Relationship to Lie algebras and finite simple groups 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures 20C34 Representations of sporadic groups 20D08 Simple groups: sporadic groups 17D99 Other nonassociative rings and algebras