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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Free summands of conormal modules and central elements in homotopy Lie algebras of local rings


Author: Srikanth Iyengar
Journal: Proc. Amer. Math. Soc. 129 (2001), 1563-1572
MSC (1991): Primary 13C15, 13D03, 13D07, 18G15
Published electronically: February 2, 2001
MathSciNet review: 1707520
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Abstract | References | Similar Articles | Additional Information

Abstract:

If $(Q,\mathfrak{n})\twoheadrightarrow (R,\mathfrak{m})$ is a surjective local homomorphism with kernel $I$, such that $I\subseteq\mathfrak{n}^2$ and the conormal module $I/I^2$ has a free summand of rank $n$, then the degree $2$ central subspace of the homotopy Lie algebra of $R$ has dimension greater than or equal to $n$. This is a corollary of the Main Theorem of this note. The techniques involved provide new proofs of some well known results concerning the conormal module.


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Additional Information

Srikanth Iyengar
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Address at time of publication: Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, United Kingdom
Email: iyengar@math.missouri.edu, s.iyengar@shef.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05565-4
PII: S 0002-9939(01)05565-4
Keywords: Homotopy Lie algebra, central elements, conormal module
Received by editor(s): April 7, 1999
Received by editor(s) in revised form: May 12, 1999
Published electronically: February 2, 2001
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2001 American Mathematical Society