What Is a Lie Group Without an Identity Matrix Called?

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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?
 
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If there is no identity then there are no inverses, so at best you'll be left with a semigroup.
 
thanks! "Semigroup" led me to "magma", which is more the generalized concept I was thinking of. <3 Wiki.
 

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