Metabelian Lie powers of the natural module for a general linear group
نویسندگان
چکیده
منابع مشابه
Lie Powers of the Natural Module for GL 2
Let L be a free Lie algebra of finite rank r over a field . For each positive integer n, denote the degree n homogeneous component of L by L. The group of graded algebra automorphisms of L may be identified with GLr; in such a way that L1 becomes the natural module, and then the L are referred to as the Lie powers of this module. Understanding the GLr; -module structure of the L may be tho...
متن کاملThe Lie Module of the Symmetric Group
We provide an upper bound of the dimension of the maximal projective submodule of the Lie module of the symmetric group of n letters in prime characteristic p, where n = pk with p k.
متن کاملModule Structure on Lie Powers and Natural Coalgebra-split Sub Hopf Algebras of Tensor Algebras
In this article, we investigate the functors from modules to modules that occur as the summands of tensor powers and the functors from modules to Hopf algebras that occur as natural coalgebra summands of tensor algebras. The main results provide some explicit natural coalgebra summands of tensor algebras. As a consequence, we obtain some decompositions of Lie powers over the general linear groups.
متن کاملOn the Classification of Metabelian Lie Algebras(')
The classification of 2-step nilpotent Lie algebras is attacked by a generator-relation method. The main results are in low dimensions or a small number of relations. Introduction. According to a theorem of Levi, in characteristic zero a finitedimensional Lie algebra can be written as the direct sum of a semisimple subalgebra and its unique maximal solvable ideal. If the field is algebraically ...
متن کاملinvestigating the feasibility of a proposed model for geometric design of deployable arch structures
deployable scissor type structures are composed of the so-called scissor-like elements (sles), which are connected to each other at an intermediate point through a pivotal connection and allow them to be folded into a compact bundle for storage or transport. several sles are connected to each other in order to form units with regular polygonal plan views. the sides and radii of the polygons are...
ذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2012
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2011.11.021