Talk:Unipotent

You define a unipotent element as being an element of a ring and then say 'A unipotent algebraic group is one all of whose elements are unipotent' without saying what it means for an element of an algebraic group to be unipotent. 131.111.1.66 (talk) 09:40, 29 April 2009 (UTC)

True; this is confusing. In this case, algebraic groups are considered to be matrix groups. —Preceding unsigned comment added by 41.185.117.226 (talk) 21:04, 10 September 2010 (UTC)

Regarding the condition $det(A)\neq 0$ in "Definition with matrices"

Maybe I am missing something here but it seems to me that the condition $det(A)\neq 0$ used while defining unipotent upper-triangular matrices and subsequently in the corresponding group scheme is redundant. Also, the cited "Unipotent algebraic groups" by J. Milne does not use the determinant in its corresponding definition.

Decomposition of algebraic groups assumes commutative

It seems to me that the statements of this section only apply for commutative algebraic groups (as assumed in the reference given). For example, $SL_{n}$ would not admit such a decomposition as an extension of an abelian variety by multiplicative and unipotent groups. The general analogue would be Chevalley's structure theorem (Theorem 1.1 here ). Quevenski (talk) 13:15, 29 October 2020 (UTC)

References

Terminology $U_{n}$

The article uses $\mathbb {U} _{n}$ for the group of upper-triangular matrices. This contrasts pretty severely with the notation $U(n)$ for the unitary group; this is close enough in area that it seems pretty confusing. Is there an alternate notation that could be used? Dylan Thurston (talk) 13:42, 1 May 2023 (UTC)