# Tagged Questions

461 views

### Structure of the adjoint representation of a (finite) group (Hopf algebra) ?

Every group acts on itself by conjugation $h \mapsto g h g^{-1}$. Respectively considering functions on a group we obtain a linear representation. Question 1: what is known about this representation ...
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### Equivalence between Algebraic Semi-group Structures and Coalgebra Structures for an Algebraic Variety?

I was looking at this old question Hopf algebra and group structure correspondence for algebraic varieties which says that there exists an equivalence between algebraic group structures on an ...
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### What happens geometrically when you take associated-graded (or complete, …) of a group ring at its augmentation ideal?

I am interested in the following functor from Monoids (in $\text{Set}$) to Graded Lie Algebras (over a fixed field of characteristic $0$). (By "graded" I mean only that my Lie algebras have some ...
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### Twist of a group Hopf-algebra

Let $G$ be a finite group with identity element $e$, and $C[G]$ the ring of complex-valued functions on $G$, with pointwise addition and multiplication. Then $C[G]$ is naturally a Hopf algebra, with ...
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### Cocyles for abelian extensions

Suppose we have an abelian extension of Hopf algebras, $$k \rightarrow k^G \rightarrow A \rightarrow kF \rightarrow k.$$ According to the general theory there is a left action of $F$ on $G$ and a ...
Please excuse, very naive question: Suppose $g$ is a topological Lie algebra over Q and $G$ = $exp(g)$ the associated group (take free group on formal symbols $exp(X)$, X $\in$ $G$, and impose all ...
Related to a previous question I am asking furthermore a proof for the following: Question 1: If $\chi$ is a faithful irreducible character of a finite group $G$ then the regular character of $G$ is ...