On the dimension of products of homogeneous subspaces in free Lie algebras
Yazarlar (2)
Doç. Dr. Nil MANSUROĞLU Ahi Evran Üniversitesi, Türkiye
Ralph Stöhr
| Bildiri Türü |
Tebliğ/Bildiri
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Bildiri Dili | İngilizce |
| Bildiri Alt Türü | Özet Metin Olarak Yayınlanan Tebliğ (Uluslararası Kongre/Sempozyum) | ||
| Bildiri Niteliği | Alanında Hakemli Uluslararası Kongre/Sempozyum | ||
| Kongre Adı | 3. International Symposium on Groups, Algebra and Relations | ||
| Kongre Tarihi | 10-06-2013 / 16-06-2013 | ||
| Basıldığı Ülke | Çin Halk Cumhuriyeti | Basıldığı Şehir | Beijing |
| Özet |
| Let L be a free Lie algebra of finite rank over a field K and let Ln denote the degree n homogeneous component of L. Formulae for the dimension of the subspaces [Lm, Ln] for all m and n were obtained by the second author and Michael Vaughan-Lee. In this note we consider subspaces of the form [Lm, Ln, Lk] = [[Lm, Ln], Lk]. 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 [L2, L2, L1] 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 [Lm, Ln, Lk]. 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 [Lm, Ln, Lk] in terms of Witt's dimension function. |
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