Michael Penkava: A new look on algebra extensions

Abstract: As a first step in generalizing the theory of algebra extensions to infinity algebras, writing everything in the language of codifferentials is useful. In the process, some new manners of expressing the theory in terms of cohomology of codifferentials was given by the speaker and Alice Fialowski, which gives an algorithmic method of computing moduli spaces of extensions. We recently applied this methodology to study the moduli space of 3-dimensional associative and 5-dimensional Lie algebras. One advantage of this approach is that it aids in the decomposition of the moduli space in terms of a stratification by projective orbifolds. The authors conjecture that such a stratification exists for the moduli space of associative and Lie algebras of a fixed, finite dimension, and have been able to verify this conjecture in low dimensions.