### Questions (32)

 6 Is the sum of coroots the coroot of the sum? 5 Show that the following function is differentiable 4 Property of a kite inscribed in a square 3 Isomorphism between adjoint and coadjoint representations 3 Prove that the following quotients are isomorphic

### Reputation (571)

 +18 A counterexample to Weyl theorem on complete reducibility +10 Angle between smooth submanifolds +10 Isomorphism between adjoint and coadjoint representations +10 Property of a kite inscribed in a square

 2 Eigenvalues of a matrix whose square is zero 1 Show that $R$ is self-injective iff every finitely generated projective right $R$-module is injective 1 an element of the Weyl group fixing a vector in the fundamental Weyl chamber 1 Prove that if $\textsf V$ is finite-dimensional, then $\textsf V = \operatorname{im}(\textsf T) \oplus \ker(\textsf T)$ 1 Remainder operator of polynomials

### Tags (55)

 4 linear-algebra × 15 1 abstract-algebra × 13 2 matrices × 2 1 modules × 8 2 eigenvalues-eigenvectors × 2 1 lie-algebras × 8 2 matrix-equations 1 injective-module × 4 2 nilpotence 1 ring-theory × 4

### Bookmarks (4)

 4 $M$ is a flat $R$-module if and only if its character module, i.e. $\hom_{\mathbb{Z}}(M,\mathbb{Q/Z})$, is injective. 2 Endomorphism $\phi: M_{n}(\mathbb{C}) \rightarrow M_{n}(\mathbb{C})$ that stabilizes $GL_{n}(\mathbb{C}).$ 2 Boundedness of a linear functional 1 Irreducible Lie algebra representation without highest weight