Combinatorics & algebra seminar- Simple simplicial algebras

Title: Simple simplicial algebras
Speaker: James Zhang, U. Washington
Date and time: Wednesday, September 30, 2:55–3:55 pm
Place: Smith 115

Abstract:  Simplicial commutative algebras act as natural resolutions in non-abelian homological algebra, bridging classical algebra and homotopy theory. They have been used extensively in deformation theory and moduli spaces; classically, simplicial methods apply to Hochschild (co)homologies, where they encode infinitesimal, higher-order, and formal deformations of algebraic structures. Noncommutative simplicial algebras are expected to deeply impact the study of noncommutative algebra and noncommutative algebraic geometry through simplicial resolutions and A_∞-structures. Because simple simplicial algebras serve as the fundamental building blocks of the theory, understanding them is a crucial first step toward uncovering the structure of general simplicial algebras. In this talk, we classify simple simplicial algebras in terms of ordinary simple algebras. This main result also applies to Lie, Jordan, and Poisson algebras.