Free summands of conormal modules and central elements in homotopy Lie algebras of local rings
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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.References
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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
- MR Author ID: 616284
- ORCID: 0000-0001-7597-7068
- Email: iyengar@math.missouri.edu, s.iyengar@shef.ac.uk
- 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
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 1563-1572
- MSC (1991): Primary 13C15, 13D03, 13D07, 18G15
- DOI: https://doi.org/10.1090/S0002-9939-01-05565-4
- MathSciNet review: 1707520