## 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.