Lie Powers of the Natural Module for GL(2)
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...
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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.
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Let G be a group, F a field of prime characteristic p and V a finite-dimensional FGmodule. Let L(V ) denote the free Lie algebra on V regarded as an FG-submodule of the free associative algebra (or tensor algebra) T (V ). For each positive integer r, let Lr(V ) and T r(V ) be the rth homogeneous components of L(V ) and T (V ), respectively. Here Lr(V ) is called the rth Lie power of V . Our mai...
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نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.
15 صفحه اولLie powers of relation modules for groups
Article history: Received 20 November 2008 Available online 17 November 2009 Communicated by Peter Webb In memoriam Karl Gruenberg
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2000
ISSN: 0021-8693
DOI: 10.1006/jabr.1998.7904