## Graded Lie algebras of maximal class. II.(English)Zbl 0971.17015

This paper refines results of an earlier paper [Trans. Am. Math. Soc. 349, 4021-4051 (1997; Zbl 0895.17037] by the authors and S. Mattarei. They describe the isomorphism classes of infinite-dimensional Lie algebras $$L = \bigoplus_{i=1}^\infty L_i$$ over a field of characteristic $$p$$ such that $$\dim L_1 = 2$$ and $$[L_i, L_1] = L_{i+1}$$ for $$i \geqq 1$$. The construction of such algebras makes use of Albert-Frank-Shalev algebras and inflation steps (concepts introduced in the earlier paper). A computer has been used in many of the calculations.
Reviewer: G.Brown (Boulder)

### MSC:

 17B70 Graded Lie (super)algebras 17B65 Infinite-dimensional Lie (super)algebras 17-04 Software, source code, etc. for problems pertaining to nonassociative rings and algebras 17B50 Modular Lie (super)algebras