Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Free ideals of one-relator graded Lie algebras
HTML articles powered by AMS MathViewer

by John P. Labute PDF
Trans. Amer. Math. Soc. 347 (1995), 175-188 Request permission

Abstract:

In this paper we show that a one-relator graded Lie algebra $\mathfrak {g} = L/(r)$, over a principal ideal domain $K$, has a homogeneous ideal $\mathfrak {h}$ with $\mathfrak {g}/\mathfrak {h}$ a free $K$-module of finite rank if the relator $r$ is not a proper multiple of another element in the free Lie algebra $L$. As an application, we deduce that the center of a one-relator Lie algebra over $K$ is trivial if the rank of $L$ is greater than two. As another application, we find a new class of one-relator pro-$p$-groups which are of cohomological dimension $2$.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 17B01, 17B70
  • Retrieve articles in all journals with MSC: 17B01, 17B70
Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 347 (1995), 175-188
  • MSC: Primary 17B01; Secondary 17B70
  • DOI: https://doi.org/10.1090/S0002-9947-1995-1282891-0
  • MathSciNet review: 1282891