An element of a Hopf algebra is called grouplike if $\Delta(g)=g\otimes g$.

learn more… | top users | synonyms

0
votes
0answers
23 views

Looking for an element in a finite abelian group $G$ which is the square of more than two elements of orders $m\geq 3$ in $G$?

Please do we have an element in a finite abelian group $G$ which is the square of more than two elements of orders $m\geq 3$ in $G$? For example in $Q_8$ which is non-abelian, all the elements in ...
4
votes
3answers
128 views

Examples of loops which have two-sided inverses.

Are there any neat examples of non-associative loops such that for each element a in the loop there exists $a^{-1}$ so that $a*a^{-1}=1=a^{-1}*a$. Even cooler would be a commutative loop. Also: are ...
4
votes
1answer
123 views

When do counital coalgebras have a basis of grouplike elements?

Question. Under what conditions do counital coalgebras have bases consisting entirely of grouplike elements? At least in the case of finite-dimensional coalgebras, or for bialgebras (or Hopf ...