Abstract
We discuss the notion of singular formal deformation in algebraic setup. Such deformations show up in both finite and infinite dimensional structures. It turns out that there is a stronger version of singular deformation—called essentially singular—which arises from a singular curve in the base of the versal deformation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Fialowski A.: Deformations of the Lie algebra of vector fields on the line. Russian Math. Surveys 38, 185–186 (1983)
A. Fialowski, An example of formal deformations of Lie algebras, NATO Conference on Deformation Theory of Algebras and Appl., Il ciocco, Italy. Proceedings Kluwer 1988, 375–401.
A. Fialowski and D.B. Fuchs, Singular Deformations of Lie algebras. Example: Deformations of the Lie algebra L 1, Topics in Singularity Theory: V.I. Arnold's 60th Anniv. Coll., Transl. Amer. Math. Soc. Ser 2 180 (1997), 77–92.
Fialowski A., Penkava M.: Versal deformations of three-dimensional Lie algebras, as \({L_{\infty}}\) algebras. Comm. in Contemp. Math. 7, 145–165 (2005)
Fialowski A., Penkava M.: Versal deformations of four dimensional Lie algebras. Comm. in Contemp. Math. 9, 41–79 (2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fialowski, A., Penkava, M. On singular formal deformations. Arch. Math. 106, 431–438 (2016). https://doi.org/10.1007/s00013-016-0894-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00013-016-0894-2