On the Hopf algebra of multi-complexes

Abstract: Hopf algebras appear naturally in combinatorics in the following way: For a given class of combinatorial objects (such as graphs or matroids), basic operations (such as assembly and disassembly operations) often can be encoded in the algebraic structure of a Hopf algebra. One then hopes to use algebraic identities of a Hopf algebra to return to combinatorial identities of combinatorial objects of interest. In this talk, I will introduce a general class of combinatorial objects, which we call multi-complexes. They simultaneously generalize graphs, hypergraphs and simplicial and delta complexes. I will describe the structure of the Hopf algebra of multi-complexes by finding an explicit basis of the space of primitives. This is joint work with Miodrag Iovanov.

machine learningcommutative algebraalgebraic geometryalgebraic topologycombinatoricscategory theoryoperator algebrasrings and algebrasrepresentation theory

Audience: researchers in the topic

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Algebraic and Combinatorial Perspectives in the Mathematical Sciences

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