What Is a Lie Group Without an Identity Matrix Called?

[Pythagorean]

Is there a name for studying a Lie "group" that doesn't use the identity matrix as a member of the group?

I know it's not technically a group anymore, but is there any mathematical work pertaining to the general idea... and what is the terminology so that I can research it better?

 

[CaffeineJunky]

If there is no identity then there are no inverses, so at best you'll be left with a semigroup.

 

[Pythagorean]

thanks! "Semigroup" led me to "magma", which is more the generalized concept I was thinking of. <3 Wiki.

 

[George Jones]

According to an article by John Baez, which may seem a little abstract (but actually is quite cool), "A torsor is like a group that has forgotten its identity."

http://math.ucr.edu/home/baez/torsors.html