There are two different approaches to the definition of left and right ideologies. One focuses on the role of the individual, and the second on the authority. In the first, the right sees the individual as the primary unit in a society that all rights and obligations must be built around. The left views the individual as a sub-unit of a larger society with rules that advance those larger interests. In that individualism versus collectivism definition, anarcho-capitalism would be on the far right, while Marxism is on the far left.
Another way to look at it is through the nature of authority. This is liberty versus order kind of perspective. The left is all about maximizing the freedom of a society, while the right is about enforcing order or harmony. In this definition, autonomism would be at the far left, while fascism is on the far right. Other examples are social libertarianism for the left, and theocracy for the right.
Keep in mind that real-world systems usually combine elements from both, like communism's combination of collectivism and authoritarianism. But philosophically speaking, leftist ideals from both branches will appeal to American liberals, while rightist ideas to conservatives.
Another way to look at it is through the nature of authority. This is liberty versus order kind of perspective. The left is all about maximizing the freedom of a society, while the right is about enforcing order or harmony. In this definition, autonomism would be at the far left, while fascism is on the far right. Other examples are social libertarianism for the left, and theocracy for the right.
Keep in mind that real-world systems usually combine elements from both, like communism's combination of collectivism and authoritarianism. But philosophically speaking, leftist ideals from both branches will appeal to American liberals, while rightist ideas to conservatives.