Let $F:A\to A'$ be a (full) exact embedding of abelian categories. When $D(F):D(A)\to D(A')$ (or its bounded version) is a full embedding also? I would be interested in any neces …

Let $G_{n}=GL(n,F)$, where $F$ a locally compact non-Archimedean field, $St_{G_{n}}$ the Steinberg representation of $G_{n}$, and $B$ the standard Borel subgroup of $G_{n}$. We de …

I got stuck in an apparently trivial point within the proof of Lemma 3.13 on p. 55 of Knapp's Representation Theory of Semisimple Groups. The author concludes in the first paragrap …

Let A be a finite dimensional algebra over a field k and M,N a finitely generated A-module. Im searching for examples where the module $ Ext^{o} (M,N) $ is a finitely generated $ …

I have a question regarding Cartan involutions of su(n). Some sources say that there is only one up to equivalence (Wikipedia on Cartan Decomposition). Others say there are Types I …

I asked this on math.stackexchange.com, but didn't get any answer. Let $\mathcal{A}$ be an abelian category and $\mathcal{C}$ a localizing subcategory in the sense of Gabriel. (A …

I am working on a paper of R.P Langlands called "Representations of abelian algebraic groups", available here: http://www.sunsite.ubc.ca/DigitalMathArchive/Langlands/pdf/AbelianAlg …

In the category of $\mathbb{Z}$-modules, there exists a module $A$---for instance $\bigoplus_{k=2}^\infty \mathbb{Z}/k\mathbb{Z}$---such that a $\mathbb{Z}$-module $B$ is injective …

Let $A \to B$ be a finitely generated homomorphism between two commutative noetherian rings. As far as I understand, in various generalizations of this situation, such a map is ca …

Let $\mathcal A$ be an abelian category with enough projectives. Consider a morphism $f \colon X^\bullet \longrightarrow Y^\bullet$ in the category $C(\cal A)$ of chain complexes i …

Let $V:=\oplus_{j\in\mathbb{Z}}V_j$ be a graded $\mathbb{F}$-vector space over the field $\mathbb{F}$. The graded tensor product of graded vector spaces is given by $V \otimes W: …

Let $\scr A$ be an abelian category with exact products and a cogenerator (e.g. $\scr A$ is a category of modules). Let ${\mathbf K}(\scr A)$ be the homotopy category of cochain c …

Let $G$ be a linear algebraic group over field $k$ of characteristic zero. It is well known that the category of finite dimensional $k$--linear representations of $G$ is abelian, a …

Hi: When I read the book "An introduction to Homological algebra" by Weibel, the page 206, line 9 says that "Shapiro's Lemma tell us that $H_q(S_n(X)\otimes_{Z}A)$ is zero if $ …

Hy guys. I'm doing some independent analysis which makes use of the tensor product of modules (over commutative rings with unit 1, and ring homomorphisms map $1 \mapsto 1$). Let $\ …