THE MODULI SPACE OF 1|1-DIMENSIONAL COMPLEX ASSOCIATIVE ALGEBRAS

Hochschild Cohomology and Moduli Spaces of Strongly Homotopy Associative Algebras

Motivated by ideas from stable homotopy theory we study the space of strongly homotopy associative multiplications on a two-cell chain complex. In the simplest case this moduli space is isomorphic to the set of orbits of a group of invertible power series acting on a certain space. The Hochschild cohomology rings of resulting A∞-algebras have an interpretation as totally ramified extensions of ...

Homotopy G - Algebras and Moduli Space

This paper emphasizes the ubiquitous role of moduli spaces of algebraic curves in associative algebra and algebraic topology. The main results are: (1) the space of an operad with multiplication is a homotopy G(i.e., homotopy graded Poisson) algebra; (2) the singular cochain complex is naturally an operad; (3) the operad of decorated moduli spaces acts naturally on the de Rham complex ΩX of a K...

The Moduli Space of Complex Lagrangian Submanifolds

The Moduli Space of 6-dimensional 2-step Nilpotent Lie Algebras

We determine the moduli space of metric 2-step nilpotent Lie algebras of dimension up to 6. This space is homeomorphic to a cone over a 4-dimensional contractible simplicial complex.

The Moduli Space of Commutative Algebras of Finite Rank

The moduli space of rank-n commutative algebras equipped with an ordered basis is an affine scheme Bn of finite type over Z, with geometrically connected fibers. It is smooth if and only if n ≤ 3. It is reducible if n ≥ 8 (and the converse holds, at least if we remove the fibers above 2 and 3). The relative dimension of Bn is 2 27 n +O(n). The subscheme parameterizing étale algebras is isomorph...