subcoalgebras and coideals
Let be a coalgebra over a field .
Definition. Vector subspace is called subcoalgebra iff .
Definition. Vector subspace is is called coideal iff and .
One can show that if is a subcoalgebra, then is also a coalgebra. On the other hand, if is a coideal, then we can cannoicaly introduce a coalgebra structure on the quotient space . More precisely, if and , then we define
and as . One can show that these two maps are well defined and is a coalgebra.
|Title||subcoalgebras and coideals|
|Date of creation||2013-03-22 18:49:19|
|Last modified on||2013-03-22 18:49:19|
|Last modified by||joking (16130)|