Year: 2026
Type: article
Abstract: We introduce a new multiplication for the polytope algebra, defined via the intersection of polytopes.After establishing the foundational properties of this intersection product, we investigate finite-dimensional subalgebras that arise naturally from this construction.These subalgebras can be regarded as volumetric analogues of the graded Möbius algebra, which appears in the context of the Dowling-Wilson conjecture.We conjecture that they also satisfy the injective hard Lefschetz property and the Hodge-Riemann relations, and we prove these in degree one.
Source: Canadian Journal of Mathematics
Author: Thomas Wannerer
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4415066755