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THE STRUCTURE OF THIN LIE ALGEBRAS WITH CHARACTERISTIC TWO.
- Source :
-
International Journal of Algebra & Computation . Sep2010, Vol. 20 Issue 6, p731-768. 38p. - Publication Year :
- 2010
-
Abstract
- Thin Lie algebras are graded Lie algebras $L = \oplus_{i = 1}^{\infty}L_{i}$ with dim Li ≤ 2 for all i, and satisfying a more stringent but natural narrowness condition modeled on an analogous condition for pro-p-groups. The two-dimensional homogeneous components of L, which include L1, are named diamonds. Infinite-dimensional thin Lie algebras with various diamond patterns have been produced, over fields of positive characteristic, as loop algebras of suitable finite-dimensional simple Lie algebras, of classical or of Cartan type depending on the location of the second diamond. The goal of this paper is a description of the initial structure of a thin Lie algebra, up to the second diamond. Specifically, if Lk is the second diamond of L, then the quotient L/Lk is a graded Lie algebras of maximal class. In odd characteristic p, the quotient L/Lk is known to be metabelian, and hence uniquely determined up to isomorphism by its dimension k, which ranges in an explicitly known set of possible values: 3, 5, a power of p, or one less than twice a power of p. However, the quotient L/Lk need not be metabelian in characteristic two. We describe here all the possibilities for L/Lk up to isomorphism. In particular, we prove that k + 1 equals a power of two. [ABSTRACT FROM AUTHOR]
- Subjects :
- *LIE algebras
*MATHEMATICS
*LINEAR algebra
*EXPONENTS
*ABSTRACT algebra
Subjects
Details
- Language :
- English
- ISSN :
- 02181967
- Volume :
- 20
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- International Journal of Algebra & Computation
- Publication Type :
- Academic Journal
- Accession number :
- 54301259
- Full Text :
- https://doi.org/10.1142/S0218196710005820