2006/10/13 by Dev Sinha, Sinha, Dev, Ben Walter +1 · 1 citation
Mathematics · #16E40 #55P48 #55P62 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.math/0610437
openalex publication_date 2006/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop a new, intrinsic, computationally friendly approach to Lie coalgebras through graph coalgebras, which are new and likely to be of independent interest. Our graph coalgebraic approach has advantages both in finding relations between coalgebra elements and in having explicit models for linear dualities. As a result, proofs in the realm of Lie coalgebras are often simpler to give through graph coalgebras than through classical methods, and for some important statements we have only found proofs in the graph coalgebra setting. For applications, we investigate the word problem for Lie coalgebras, we revisit Harrison homology, and we unify the two standard Quillen functors between differential graded commutative algebras and Lie coalgebras.