Search arXiv⌕ Search

arXiv · 0707.2167

An explicit formula for the action of a finite group on a commutative ring

Abstract

Let G be a group which acts on a commutative ring k. We exhibit an induction formula which expresses an element x_G with tr_G(x_G)=1 by elements x_P with tr_P(x_P)=1, where P varies over prime order subgroups of P.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ehud Meir. 2007-07-14. An explicit formula for the action of a finite group on a commutative ring. https://arxiv.org/abs/0707.2167

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Multilinear nilalgebras and the Jacobian theorem

If a symmetric multilinear algebra is weakly nil, then it is Engel. This result may be regarded as an infinite-dimensional analogue of the well-known Jacobian theorem, which states that if a polynomial mapping has a polynomial inverse, then its Jacobian matrix is invertible. This refines a theorem of Gerstenhaber and partially answers a question posed by Dotsenko.

math.RA↗

Local (Anti-)Superderivations on Nilpotent Lie Superalgebras

In this paper, we study local superderivations and local anti-superderivations of finite-dimensional nilpotent Lie superalgebras over a field $\mathbb F$ with $\operatorname{char}\mathbb F\neq2$. First, we prove that every finite-dimensional two-step nilpotent Lie superalgebra admits pure local superderivations and pure local anti-superderivations (namely, local (anti-)superderivations that are not (anti-)superderivations). For nilpotent Lie superalgebras of nilpotency index greater than two, we establish sufficient conditions for the existence of pure local superderivations and pure local anti-superderivations. In particular, we prove that every three-step nilpotent Lie superalgebra admits a pure local superderivation.

math.RA↗