On the dimension of products of homogeneous subspaces in free Lie algebras
Yazarlar (2)
Doç. Dr. Nil MANSUROĞLU
The University Of Manchester, İngiltere
Ralph Stöhr
The University Of Manchester, İngiltere
| Makale Türü | Özgün Makale (SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale) | ||
| Dergi Adı | International Journal of Algebra and Computation | ||
| Dergi ISSN | 0218-1967 Wos Dergi Scopus Dergi | ||
| Dergi Tarandığı Indeksler | SCI-Expanded | ||
| Makale Dili | İngilizce | Basım Tarihi | 02-2013 |
| Cilt / Sayı / Sayfa | 23 / 1 / 205–213 | DOI | 10.1142/S0218196713500069 |
| Özet |
| Let L be a free Lie algebra of finite rank over a field K and let L-n denote the degree n homogeneous component of L. Formulae for the dimension of the subspaces [L-m, L-n] for all m and n were obtained by the second author and Michael Vaughan-Lee. In this note we consider subspaces of the form [L-m, L-n, L-k] = [[L-m, L-n], L-k]. Surprisingly, in contrast to the case of a product of two homogeneous components, the dimension of such products may depend on the characteristic of the field K. For example, the dimension of [L-2, L-2, L-1] over fields of characteristic 2 is different from the dimension over fields of characteristic other than 2. Our main results are formulae for the dimension of [L-m, L-n, L-k]. Under certain conditions on m, n and k they lead to explicit formulae that do not depend on the characteristic of K, and express the dimension of [L-m, L-n, L-k] in terms of Witt's dimension function. |
| Anahtar Kelimeler |
| Free Lie algebras | homogeneous subspaces |