Google fully works with the .google.com domain, so they have absolutely no problem using a single cookie to identify you across all applications. If your applications all work in the same domain, I would say go ahead and create your own version to authorize users with a shared session cookie.
However, in the more likely case, if this is not the case, you are better off implementing one of the most popular and widespread single sign-on methodologies, for example OAuth or OpenID separately in your applications and providing your users with a centralized authentication application or allowing them to authenticate through external providers ( e.g. Facebook or Google, which supports authentication via OpenID)
You can run your own OAuth or OpenID endpoint at which your users register and then log in through that endpoint in any of your applications.
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