User:Dfeuer/Definition:Total Positive Cone
Jump to navigation
Jump to search
Definition
Let $(G,\circ)$ be a group.
Let $P$ be a Positive Cone $(G,\circ)$.
Then $P$ is a total positive cone or weak total positive cone iff:
- $P \cup P^{-1} = G$
That is, $P$ is a total positive cone for $G$ if $P$ is a subset of $G$ such that:
- $x,y \in P \implies x \circ y \in P$
- $x \circ y \in P \implies y \circ x \in P$
- $P \cap P^{-1} = \{e\}$
- $P \cup P^{-1} = G$