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 [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] = [[L m, 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. © 2013 World Scientific Publishing Company.
Anahtar Kelimeler
Free Lie algebras | homogeneous subspaces
Science Direct
Atıf Sayıları
Scopus 2
Web of Science 3
On the dimension of products of homogeneous subspaces in free Lie algebras

Paylaş

İletişim
  • Kırşehir Ahi Evran Üniversitesi Bağbaşı Yerleşkesi, 40100, KIRŞEHİR \ TÜRKİYE
  • unis@ahievran.edu.tr
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