A Characterization of Linearly Semisimple Groups

作者：Alvarez Amelia^*; Sancho Pedro; Sancho Carlos

来源：Acta Mathematica Sinica-English Series, 2011, 27(1): 185-192.

DOI：10.1007/s10114-011-8658-1

• Linearly reductive group
• trace form
• Pontrjagin's duality

Let G = Spec A be an affine K-group scheme and (A) over tilde = {w is an element of A*: dim(K) A* w < infinity, dim(K) w A* < infinity}. Let <-, -> : A* x (A) over tilde K, < w, (w) over tilde > := tr(w (w) over tilde), be the trace form. We prove that G is linearly reductive if and only if the trace form is non-degenerate on A*.

• 出版日期2011-1