Deformations of Complex 3-Dimensional Associative AlgebrasAlice Fialowski1, Michael Penkava2 and Mitch Phillipson2
1Institute of Mathematics, E¨otv¨os Lor´and University, 1053 Budapest, Hungary. Email: [email protected]
Received Date: 27 August 2010; Accepted Date: 26 January 2011
We study deformations and the moduli space of 3-dimensional complex associative algebras. We use extensions to compute the moduli space, and then give a decomposition of this moduli space into strata consisting of complex projective orbifolds, glued together through jump deformations. The main purpose of this paper is to give a logically organized description of the moduli space, and to give an explicit description of how the moduli space is constructed by extensions.