3
$\begingroup$

Let $V=\Bbb R^n$. Morelli defined the (commutative unital) ring $L(V)$ to be the additive group generated by the indicator functions of convex polytopes in $V$ with multiplication induced by Minkowski sum.

Let $P$ be a convex polytope in $V$, and consider the subring $A(P)$ of $L(V)$ generated by the faces of $P$ (including $P$ itself).

Question: Has $A(P)$ been studied at all?

Improve this question
$\endgroup$
1
  • 1
    $\begingroup$ Beside (and probably before) Morelli the "big" algebraic structure was studied by Peter McMullen (algebra of polytopes) and Pukhlikov - Khovanskii (virtual polytopes). $\endgroup$
    – Ivan Izmestiev
    Commented Nov 20, 2018 at 18:32

0

Reset to default

You must log in to answer this question.