Derivation of the Tensor-Products of ?? -algebras

Abstract

A?B가 C?-대수일 때, A 혹은 B 가 외부미분(outer derivation)을 갖으면 A?B는 외부 미분을 갖는다. 이 논문에서는 A, B가 모두 내부미분(inner derivation)만을 갖는 경우 중 A가 Von Neumann대수이고 B가 가환 C?-대수일 때 A?B가 내부미분만을 갖음을 보였다.

Let A and B be C?-algebras. If A ro B has outer derivations, A?B has outer derivations. Among the case of A and B with only inner derivations, we are going to show that if A is a Von Neuman algebra and B is a commutative algebra, then every derivation of A?B is inner.

Let A and B be C?-algebras. If A ro B has outer derivations, A?B has outer derivations. Among the case of A and B with only inner derivations, we are going to show that if A is a Von Neuman algebra and B is a commutative algebra, then every derivation of A?B is inner.